Writing power series as function
0
$begingroup$
I need to write the following power series as a function:
$2sum_{n=0}^infty (-1)^n x^{2n+1}$
I am not sure how to go about doing this.
calculus sequences-and-series power-series
edited Dec 8 '18 at 0:24
Foobaz John
21.7k41352
asked Dec 8 '18 at 0:07
ElijahElijah
626
$endgroup$
add a comment |
0
$begingroup$
I need to write the following power series as a function:
$2sum_{n=0}^infty (-1)^n x^{2n+1}$
I am not sure how to go about doing this.
calculus sequences-and-series power-series
edited Dec 8 '18 at 0:24
Foobaz John
21.7k41352
asked Dec 8 '18 at 0:07
ElijahElijah
626
$endgroup$
$begingroup$
Hint: use a geometric series.
$endgroup$
– Sean Roberson
Dec 8 '18 at 0:11
$begingroup$
What do you mean "write it as a function"? It's already a function with domain $|x|<1. $ I guess what you mean is "find a simple formula for this function."
$endgroup$
– zhw.
Dec 8 '18 at 1:45
add a comment |
0
0
0
$begingroup$
I need to write the following power series as a function:
$2sum_{n=0}^infty (-1)^n x^{2n+1}$
I am not sure how to go about doing this.
calculus sequences-and-series power-series
edited Dec 8 '18 at 0:24
Foobaz John
21.7k41352
asked Dec 8 '18 at 0:07
ElijahElijah
626
$endgroup$
I need to write the following power series as a function:
$2sum_{n=0}^infty (-1)^n x^{2n+1}$
I am not sure how to go about doing this.
calculus sequences-and-series power-series
calculus sequences-and-series power-series
edited Dec 8 '18 at 0:24
Foobaz John
21.7k41352
asked Dec 8 '18 at 0:07
ElijahElijah
626
edited Dec 8 '18 at 0:24
Foobaz John
21.7k41352
asked Dec 8 '18 at 0:07
ElijahElijah
626
edited Dec 8 '18 at 0:24
Foobaz John
21.7k41352
edited Dec 8 '18 at 0:24
Foobaz John
21.7k41352
edited Dec 8 '18 at 0:24
Foobaz John
21.7k41352
21.7k41352
asked Dec 8 '18 at 0:07
ElijahElijah
626
asked Dec 8 '18 at 0:07
ElijahElijah
626
asked Dec 8 '18 at 0:07
ElijahElijah
626
626
$begingroup$
Hint: use a geometric series.
$endgroup$
– Sean Roberson
Dec 8 '18 at 0:11
$begingroup$
What do you mean "write it as a function"? It's already a function with domain $|x|<1. $ I guess what you mean is "find a simple formula for this function."
$endgroup$
– zhw.
Dec 8 '18 at 1:45
add a comment |
$begingroup$
Hint: use a geometric series.
$endgroup$
– Sean Roberson
Dec 8 '18 at 0:11
$begingroup$
What do you mean "write it as a function"? It's already a function with domain $|x|<1. $ I guess what you mean is "find a simple formula for this function."
$endgroup$
– zhw.
Dec 8 '18 at 1:45
$begingroup$
Hint: use a geometric series.
$endgroup$
– Sean Roberson
Dec 8 '18 at 0:11
$begingroup$
Hint: use a geometric series.
$endgroup$
– Sean Roberson
Dec 8 '18 at 0:11
$begingroup$
What do you mean "write it as a function"? It's already a function with domain $|x|<1. $ I guess what you mean is "find a simple formula for this function."
$endgroup$
– zhw.
Dec 8 '18 at 1:45
$begingroup$
What do you mean "write it as a function"? It's already a function with domain $|x|<1. $ I guess what you mean is "find a simple formula for this function."
$endgroup$
– zhw.
Dec 8 '18 at 1:45
add a comment |
1 Answer
1
active
oldest
votes
1
$begingroup$
Hints
The sum can be written as
$$
2xsum_{n=0}^infty (-x^2)^{n}
$$
and recall the formula for a geometric series.
answered Dec 8 '18 at 0:23
Foobaz JohnFoobaz John
21.7k41352
$endgroup$
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
});
}
});
draft saved
draft discarded
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%2f3030531%2fwriting-power-series-as-function%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
1
$begingroup$
Hints
The sum can be written as
$$
2xsum_{n=0}^infty (-x^2)^{n}
$$
and recall the formula for a geometric series.
answered Dec 8 '18 at 0:23
Foobaz JohnFoobaz John
21.7k41352
$endgroup$
add a comment |
1
$begingroup$
Hints
The sum can be written as
$$
2xsum_{n=0}^infty (-x^2)^{n}
$$
and recall the formula for a geometric series.
answered Dec 8 '18 at 0:23
Foobaz JohnFoobaz John
21.7k41352
$endgroup$
add a comment |
1
1
1
$begingroup$
Hints
The sum can be written as
$$
2xsum_{n=0}^infty (-x^2)^{n}
$$
and recall the formula for a geometric series.
answered Dec 8 '18 at 0:23
Foobaz JohnFoobaz John
21.7k41352
$endgroup$
Hints
The sum can be written as
$$
2xsum_{n=0}^infty (-x^2)^{n}
$$
and recall the formula for a geometric series.
answered Dec 8 '18 at 0:23
Foobaz JohnFoobaz John
21.7k41352
answered Dec 8 '18 at 0:23
Foobaz JohnFoobaz John
21.7k41352
answered Dec 8 '18 at 0:23
Foobaz JohnFoobaz John
21.7k41352
answered Dec 8 '18 at 0:23
Foobaz JohnFoobaz John
21.7k41352
21.7k41352
add a comment |
add a comment |
draft saved
draft discarded
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.
draft saved
draft discarded
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%2f3030531%2fwriting-power-series-as-function%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
$begingroup$
Hint: use a geometric series.
$endgroup$
– Sean Roberson
Dec 8 '18 at 0:11
$begingroup$
What do you mean "write it as a function"? It's already a function with domain $|x|<1. $ I guess what you mean is "find a simple formula for this function."
$endgroup$
– zhw.
Dec 8 '18 at 1:45