npm package: @stdlib/math-base-tools-sum-series
Description: Compute the sum of an infinite series.
Author: The Stdlib Authors
Latest version: 0.2.3

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</details>

# sum-series

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

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

<section class="installation">

## Installation

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

</section>

<section class="usage">

## 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]:

<!-- eslint-disable no-restricted-syntax, node/no-unsupported-features/es-syntax -->

```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 );
    }
}
```

</section>

<!-- /.usage -->

<section class="examples">

## Examples

<!-- eslint-disable no-restricted-syntax, node/no-unsupported-features/es-syntax -->

<!-- eslint no-undef: "error" -->

```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 ) ) );
```

</section>

<!-- /.examples -->

<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->

<section class="related">

</section>

<!-- /.related -->

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<section class="main-repo" >

* * *

## 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 &copy; 2016-2026. The Stdlib [Authors][stdlib-authors].

</section>

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

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[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*

</section>

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