Evaluating a (probably) arithmetic progression The 2019 Stack Overflow Developer Survey Results Are InA tricky arithmetic progression problemA tricky arithmetic progression questionFinding numbers and Arithmetic progressionSummation and Arithmetic progression problemarithmetic progression, problem.Common term between arithmetic progressionArithmetic progression determinationHow to solve for x when function can't be invertedTrading stock arithmetic progressionSum of the inverse of a geometric series?
On the insanity of kings as an argument against Monarchy
How to change the limits of integration
Spanish for "widget"
Where to refill my bottle in India?
Deadlock Graph and Interpretation, solution to avoid
Extreme, unacceptable situation and I can't attend work tomorrow morning
Why is Grand Jury testimony secret?
aging parents with no investments
What is a mixture ratio of propellant?
Where does the "burst of radiance" from Holy Weapon originate?
Why isn't airport relocation done gradually?
If the Wish spell is used to duplicate the effect of Simulacrum, are existing duplicates destroyed?
What are the motivations for publishing new editions of an existing textbook, beyond new discoveries in a field?
Is "plugging out" electronic devices an American expression?
Does duplicating a spell with Wish count as casting that spell?
Inline version of a function returns different value then non-inline version
How come people say “Would of”?
Is there a name of the flying bionic bird?
I see my dog run
What could be the right powersource for 15 seconds lifespan disposable giant chainsaw?
It's possible to achieve negative score?
Evaluating number of iteration with a certain map with While
Carnot-Caratheodory metric
Output the Arecibo Message
Evaluating a (probably) arithmetic progression
The 2019 Stack Overflow Developer Survey Results Are InA tricky arithmetic progression problemA tricky arithmetic progression questionFinding numbers and Arithmetic progressionSummation and Arithmetic progression problemarithmetic progression, problem.Common term between arithmetic progressionArithmetic progression determinationHow to solve for x when function can't be invertedTrading stock arithmetic progressionSum of the inverse of a geometric series?
$begingroup$
Recently, I've stumbled upon an equation (9th grade) that I know nothing about. It looks like this:
$frac 1 sqrt 5+ sqrt 2+frac 1 sqrt 8+ sqrt 5 +frac 1 sqrt 11+ sqrt 8+...+frac 1 sqrt 38+ sqrt 35$
Obviously, if you continue by replacing three dots, you'll get:
$frac 1 sqrt 14+ sqrt 11 + frac 1 sqrt 17+ sqrt 14$ so on, so on until last.
But what am I supposed to do to solve this? Roughly translating from my language the task looks like: Evaluate the sum.
I mean, it doesn't look like arithmetic progression, because I am not able to find d or geometric progression to find q, so what should I do to solve it?
summation arithmetic-progressions
asked Mar 30 at 10:52
Eugen ErayEugen Eray
1084
$endgroup$
add a comment |
$begingroup$
Recently, I've stumbled upon an equation (9th grade) that I know nothing about. It looks like this:
$frac 1 sqrt 5+ sqrt 2+frac 1 sqrt 8+ sqrt 5 +frac 1 sqrt 11+ sqrt 8+...+frac 1 sqrt 38+ sqrt 35$
Obviously, if you continue by replacing three dots, you'll get:
$frac 1 sqrt 14+ sqrt 11 + frac 1 sqrt 17+ sqrt 14$ so on, so on until last.
But what am I supposed to do to solve this? Roughly translating from my language the task looks like: Evaluate the sum.
I mean, it doesn't look like arithmetic progression, because I am not able to find d or geometric progression to find q, so what should I do to solve it?
summation arithmetic-progressions
asked Mar 30 at 10:52
Eugen ErayEugen Eray
1084
$endgroup$
add a comment |
$begingroup$
Recently, I've stumbled upon an equation (9th grade) that I know nothing about. It looks like this:
$frac 1 sqrt 5+ sqrt 2+frac 1 sqrt 8+ sqrt 5 +frac 1 sqrt 11+ sqrt 8+...+frac 1 sqrt 38+ sqrt 35$
Obviously, if you continue by replacing three dots, you'll get:
$frac 1 sqrt 14+ sqrt 11 + frac 1 sqrt 17+ sqrt 14$ so on, so on until last.
But what am I supposed to do to solve this? Roughly translating from my language the task looks like: Evaluate the sum.
I mean, it doesn't look like arithmetic progression, because I am not able to find d or geometric progression to find q, so what should I do to solve it?
summation arithmetic-progressions
asked Mar 30 at 10:52
Eugen ErayEugen Eray
1084
$endgroup$
Recently, I've stumbled upon an equation (9th grade) that I know nothing about. It looks like this:
$frac 1 sqrt 5+ sqrt 2+frac 1 sqrt 8+ sqrt 5 +frac 1 sqrt 11+ sqrt 8+...+frac 1 sqrt 38+ sqrt 35$
Obviously, if you continue by replacing three dots, you'll get:
$frac 1 sqrt 14+ sqrt 11 + frac 1 sqrt 17+ sqrt 14$ so on, so on until last.
But what am I supposed to do to solve this? Roughly translating from my language the task looks like: Evaluate the sum.
I mean, it doesn't look like arithmetic progression, because I am not able to find d or geometric progression to find q, so what should I do to solve it?
summation arithmetic-progressions
summation arithmetic-progressions
asked Mar 30 at 10:52
Eugen ErayEugen Eray
1084
asked Mar 30 at 10:52
Eugen ErayEugen Eray
1084
asked Mar 30 at 10:52
Eugen ErayEugen Eray
1084
asked Mar 30 at 10:52
Eugen ErayEugen Eray
1084
asked Mar 30 at 10:52
Eugen ErayEugen Eray
1084
1084
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Hint: square roots in denominators are usually not nice to work with. So get rid of them: Expand the first fraction by $sqrt5-sqrt2$, the second fraction by $sqrt8-sqrt5$, and so on. Then add them together.
answered Mar 30 at 10:54
ArthurArthur
122k7122211
$endgroup$
$begingroup$
Helped out, thanks a lot!
$endgroup$
– Eugen Eray
Apr 1 at 7:12
add a comment |
Your Answer
StackExchange.ifUsing("editor", function ()
return StackExchange.using("mathjaxEditing", function ()
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix)
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
);
);
, "mathjax-editing");
StackExchange.ready(function()
var channelOptions =
tags: "".split(" "),
id: "69"
;
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function()
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled)
StackExchange.using("snippets", function()
createEditor();
);
else
createEditor();
);
function createEditor()
StackExchange.prepareEditor(
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader:
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
,
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
);
);
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3168148%2fevaluating-a-probably-arithmetic-progression%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Hint: square roots in denominators are usually not nice to work with. So get rid of them: Expand the first fraction by $sqrt5-sqrt2$, the second fraction by $sqrt8-sqrt5$, and so on. Then add them together.
answered Mar 30 at 10:54
ArthurArthur
122k7122211
$endgroup$
$begingroup$
Helped out, thanks a lot!
$endgroup$
– Eugen Eray
Apr 1 at 7:12
add a comment |
$begingroup$
Hint: square roots in denominators are usually not nice to work with. So get rid of them: Expand the first fraction by $sqrt5-sqrt2$, the second fraction by $sqrt8-sqrt5$, and so on. Then add them together.
answered Mar 30 at 10:54
ArthurArthur
122k7122211
$endgroup$
$begingroup$
Helped out, thanks a lot!
$endgroup$
– Eugen Eray
Apr 1 at 7:12
add a comment |
$begingroup$
Hint: square roots in denominators are usually not nice to work with. So get rid of them: Expand the first fraction by $sqrt5-sqrt2$, the second fraction by $sqrt8-sqrt5$, and so on. Then add them together.
answered Mar 30 at 10:54
ArthurArthur
122k7122211
$endgroup$
Hint: square roots in denominators are usually not nice to work with. So get rid of them: Expand the first fraction by $sqrt5-sqrt2$, the second fraction by $sqrt8-sqrt5$, and so on. Then add them together.
answered Mar 30 at 10:54
ArthurArthur
122k7122211
answered Mar 30 at 10:54
ArthurArthur
122k7122211
answered Mar 30 at 10:54
ArthurArthur
122k7122211
answered Mar 30 at 10:54
ArthurArthur
122k7122211
122k7122211
$begingroup$
Helped out, thanks a lot!
$endgroup$
– Eugen Eray
Apr 1 at 7:12
add a comment |
$begingroup$
Helped out, thanks a lot!
$endgroup$
– Eugen Eray
Apr 1 at 7:12
$begingroup$
Helped out, thanks a lot!
$endgroup$
– Eugen Eray
Apr 1 at 7:12
$begingroup$
Helped out, thanks a lot!
$endgroup$
– Eugen Eray
Apr 1 at 7:12
add a comment |
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3168148%2fevaluating-a-probably-arithmetic-progression%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
