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https://github.com/stdlib-js/math-base-tools-sum-series

Compute the sum of an infinite series.
https://github.com/stdlib-js/math-base-tools-sum-series

expansion fraction javascript math mathematics node node-js nodejs series stdlib

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Compute the sum of an infinite series.

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README 

        



  

    About stdlib...

  

  
We believe in a future in which the web is a preferred environment for numerical computation. To help realize this future, we've built stdlib. stdlib is a standard library, with an emphasis on numerical and scientific computation, written in JavaScript (and C) for execution in browsers and in Node.js.


  
The library is fully decomposable, being architected in such a way that you can swap out and mix and match APIs and functionality to cater to your exact preferences and use cases.


  
When you use stdlib, you can be absolutely certain that you are using the most thorough, rigorous, well-written, studied, documented, tested, measured, and high-quality code out there.


  
To join us in bringing numerical computing to the web, get started by checking us out on GitHub, and please consider financially supporting stdlib. We greatly appreciate your continued support!



# sum-series



[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url] 



> Compute the sum of an [infinite series][infinite-series].



## Installation



```bash

npm install @stdlib/math-base-tools-sum-series

```



Alternatively,



-   To load the package in a website via a `script` tag without installation and bundlers, use the [ES Module][es-module] available on the [`esm`][esm-url] branch (see [README][esm-readme]).

-   If you are using Deno, visit the [`deno`][deno-url] branch (see [README][deno-readme] for usage intructions).

-   For use in Observable, or in browser/node environments, use the [Universal Module Definition (UMD)][umd] build available on the [`umd`][umd-url] branch (see [README][umd-readme]).



The [branches.md][branches-url] file summarizes the available branches and displays a diagram illustrating their relationships.



To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.



## Usage



```javascript

var sumSeries = require( '@stdlib/math-base-tools-sum-series' );

```



#### sumSeries( generator\[, options ] )



Computes the sum of the series given by the supplied `generator` argument. `generator` can be either an ES6 [Generator object][es6-generator] or a function which returns successive elements of the series at each invocation.



Using an ES6 [Generator object][es6-generator]:



```javascript

var pow = require( '@stdlib/math-base-special-pow' );

var gen = geometricSeriesGenerator( 0.9 );

var out = sumSeries( gen );

// returns 10



function* geometricSeriesGenerator( x ) {

    var exponent = 0;

    while ( true ) {

        yield pow( x, exponent );

        exponent += 1;

    }

}

```



Alternatively, one can use a closure to achieve the same goal:



```javascript

var pow = require( '@stdlib/math-base-special-pow' );

var gen = geometricSeriesClosure( 0.9 );

var out = sumSeries( gen );

// returns 10



function geometricSeriesClosure( x ) {

    var exponent = -1;

    return gen;



    function gen() {

        exponent += 1;

        return pow( x, exponent );

    }

}

```



The `function` accepts the following `options`:



-   **maxTerms**: integer denoting the maximum number of terms to be summed. Default: `1000000`.

-   **tolerance**: number specifying the tolerance used to assess convergence. Default: `2.22e-16`.

-   **initialValue**: number specifying the initial value of the returned sum. Default: `0`.



By default, the initial value of the sum is `0`. To choose a different one, use the `initialValue` option.



```javascript

var pow = require( '@stdlib/math-base-special-pow' );



var out = sumSeries( geometricSeriesClosure( 0.5 ), {

    'initialValue': 1

});

// returns 3



function geometricSeriesClosure( x ) {

    var exponent = -1;

    return gen;



    function gen() {

        exponent += 1;

        return pow( x, exponent );

    }

}

```



To change the maximum number of terms to be summed, set the `maxTerms` option.



```javascript

var pow = require( '@stdlib/math-base-special-pow' );



// Note: infinite sum is 2

var out = sumSeries( geometricSeriesClosure( 0.5 ), {

    'maxTerms': 10

});

// returns ~1.998



function geometricSeriesClosure( x ) {

    var exponent = -1;

    return gen;



    function gen() {

        exponent += 1;

        return pow( x, exponent );

    }

}

```



The default tolerance of `2.22e-16` used to assess convergence can be changed via the `tolerance` option.



```javascript

var pow = require( '@stdlib/math-base-special-pow' );



var out = sumSeries( geometricSeriesClosure( 0.5 ), {

    'tolerance': 1e-3

});

// returns ~1.998



function geometricSeriesClosure( x ) {

    var exponent = -1;

    return gen;



    function gen() {

        exponent += 1;

        return pow( x, exponent );

    }

}

```



## Examples



```javascript

var log1p = require( '@stdlib/math-base-special-log1p' );

var sumSeries = require( '@stdlib/math-base-tools-sum-series' );



function* log1pSeries( x ) {

    var mMult = -x;

    var mProd = -1;

    var k = 0;

    while ( true ) {

        mProd *= mMult;

        k += 1;

        yield ( mProd / k );

    }

}



console.log( 'log1p(0.5) evaluated via math-log1p module: %d', log1p( 0.5 ) );

console.log( 'log1p(0.5) evaluated via infinite series expansion: %d', sumSeries( log1pSeries( 0.5 ) ) );

```



* * *



## Notice



This package is part of [stdlib][stdlib], a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.



For more information on the project, filing bug reports and feature requests, and guidance on how to develop [stdlib][stdlib], see the main project [repository][stdlib].



#### Community



[![Chat][chat-image]][chat-url]



---



## License



See [LICENSE][stdlib-license].



## Copyright



Copyright © 2016-2024. The Stdlib [Authors][stdlib-authors].



[npm-image]: http://img.shields.io/npm/v/@stdlib/math-base-tools-sum-series.svg

[npm-url]: https://npmjs.org/package/@stdlib/math-base-tools-sum-series



[test-image]: https://github.com/stdlib-js/math-base-tools-sum-series/actions/workflows/test.yml/badge.svg?branch=main

[test-url]: https://github.com/stdlib-js/math-base-tools-sum-series/actions/workflows/test.yml?query=branch:main



[coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/math-base-tools-sum-series/main.svg

[coverage-url]: https://codecov.io/github/stdlib-js/math-base-tools-sum-series?branch=main



[chat-image]: https://img.shields.io/gitter/room/stdlib-js/stdlib.svg

[chat-url]: https://app.gitter.im/#/room/#stdlib-js_stdlib:gitter.im



[stdlib]: https://github.com/stdlib-js/stdlib



[stdlib-authors]: https://github.com/stdlib-js/stdlib/graphs/contributors



[umd]: https://github.com/umdjs/umd

[es-module]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Modules



[deno-url]: https://github.com/stdlib-js/math-base-tools-sum-series/tree/deno

[deno-readme]: https://github.com/stdlib-js/math-base-tools-sum-series/blob/deno/README.md

[umd-url]: https://github.com/stdlib-js/math-base-tools-sum-series/tree/umd

[umd-readme]: https://github.com/stdlib-js/math-base-tools-sum-series/blob/umd/README.md

[esm-url]: https://github.com/stdlib-js/math-base-tools-sum-series/tree/esm

[esm-readme]: https://github.com/stdlib-js/math-base-tools-sum-series/blob/esm/README.md

[branches-url]: https://github.com/stdlib-js/math-base-tools-sum-series/blob/main/branches.md



[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/math-base-tools-sum-series/main/LICENSE



[infinite-series]: https://en.wikipedia.org/wiki/Series_%28mathematics%29



[es6-generator]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Statements/function*