---
title: 'Power Series on Desmos'
url: 'https://blog.recursiveprocess.com/2014/03/05/power-series-on-desmos'
markdown: 'https://blog.recursiveprocess.com/2014/03/05/power-series-on-desmos.md'
date: '2014-03-05'
description: 'This is a crosspost from my Photo 180 blog. Power Series work in AP Calculus BC. Process: Since it’s a infinite series, look at partial sums to get an idea what this graph looks like. So look at … Perfect time to use technology. Texas Instruments Method Go to y1. Enter in . Graph. W…'
taxonomy:
  category:
    - blog
---

### [Power Series on Desmos](https://blog.recursiveprocess.com/2014/03/05/power-series-on-desmos)

   March 5, 2014, 12:00 am  

[This is a crosspost from my Photo 180 blog](http://photo180.recursiveprocess.com/?p=1527).

Power Series work in AP Calculus BC.

![\sum_{n=0}^{\infty}(-1)^{n}\frac{x^{2n+1}}{(2n+1)!}=\frac{x}{1!}-\frac{x^3}{3!}+\frac{x^5}{5!}-...](http://s0.wp.com/latex.php?latex=%5Csum_%7Bn%3D0%7D%5E%7B%5Cinfty%7D%28-1%29%5E%7Bn%7D%5Cfrac%7Bx%5E%7B2n%2B1%7D%7D%7B%282n%2B1%29%21%7D%3D%5Cfrac%7Bx%7D%7B1%21%7D-%5Cfrac%7Bx%5E3%7D%7B3%21%7D%2B%5Cfrac%7Bx%5E5%7D%7B5%21%7D-...&bg=ffffff&fg=000&s=0&c=20201002)

Process: Since it’s a infinite series, look at partial sums to get an idea what this graph looks like.
So look at
![y_1=\frac{x}{1!}](http://s0.wp.com/latex.php?latex=y_1%3D%5Cfrac%7Bx%7D%7B1%21%7D&bg=ffffff&fg=000&s=0&c=20201002)
![y_2=\frac{x}{1!}-\frac{x^3}{3!}](http://s0.wp.com/latex.php?latex=y_2%3D%5Cfrac%7Bx%7D%7B1%21%7D-%5Cfrac%7Bx%5E3%7D%7B3%21%7D&bg=ffffff&fg=000&s=0&c=20201002)
![y_2=\frac{x}{1!}-\frac{x^3}{3!}+\frac{x^5}{5!}](http://s0.wp.com/latex.php?latex=y_2%3D%5Cfrac%7Bx%7D%7B1%21%7D-%5Cfrac%7Bx%5E3%7D%7B3%21%7D%2B%5Cfrac%7Bx%5E5%7D%7B5%21%7D&bg=ffffff&fg=000&s=0&c=20201002)
…
Perfect time to use technology.

## Texas Instruments Method

Go to y1. Enter in ![y=x](http://s0.wp.com/latex.php?latex=y%3Dx&bg=ffffff&fg=000&s=0&c=20201002).
Graph.
Wait 3-5 seconds.
Go to y1. Subtract a ![\frac{x^3}{3!}](http://s0.wp.com/latex.php?latex=%5Cfrac%7Bx%5E3%7D%7B3%21%7D&bg=ffffff&fg=000&s=0&c=20201002).
Graph.
Wait 3-5 seconds.
Go to y1. Add on a ![\frac{x^5}{5!}](http://s0.wp.com/latex.php?latex=%5Cfrac%7Bx%5E5%7D%7B5%21%7D&bg=ffffff&fg=000&s=0&c=20201002).
Graph.
Wait 3-5 seconds.
Go to y1. Subtract a ![\frac{x^7}{7!}](http://s0.wp.com/latex.php?latex=%5Cfrac%7Bx%5E7%7D%7B7%21%7D&bg=ffffff&fg=000&s=0&c=20201002).
…
[![2014-03-05_13h53_31](http://photo180.recursiveprocess.com/wp-content/uploads/2014/03/2014-03-05_13h53_31.png)](http://photo180.recursiveprocess.com/wp-content/uploads/2014/03/2014-03-05_13h53_31.png) [![2014-03-05_13h53_44](http://photo180.recursiveprocess.com/wp-content/uploads/2014/03/2014-03-05_13h53_44.png)](http://photo180.recursiveprocess.com/wp-content/uploads/2014/03/2014-03-05_13h53_44.png)

REALLY crappy resolution. Awful zoom system. Where’s the factorial sign? Hopefully you remember what the previous graphs looked like. Lots of waiting. Ugh.

## Desmos: version 1

Graph ![y=x](http://s0.wp.com/latex.php?latex=y%3Dx&bg=ffffff&fg=000&s=0&c=20201002)
(NO WAIT STEP)
Subtract a ![\frac{x^3}{3!}](http://s0.wp.com/latex.php?latex=%5Cfrac%7Bx%5E3%7D%7B3%21%7D&bg=ffffff&fg=000&s=0&c=20201002).
(STILL NO WAIT STEP)
Add on a ![\frac{x^5}{5!}](http://s0.wp.com/latex.php?latex=%5Cfrac%7Bx%5E5%7D%7B5%21%7D&bg=ffffff&fg=000&s=0&c=20201002).
Subtract a ![\frac{x^7}{7!}](http://s0.wp.com/latex.php?latex=%5Cfrac%7Bx%5E7%7D%7B7%21%7D&bg=ffffff&fg=000&s=0&c=20201002).
[![2014-03-05_13h55_46](http://photo180.recursiveprocess.com/wp-content/uploads/2014/03/2014-03-05_13h55_46-1024x442.png)](http://photo180.recursiveprocess.com/wp-content/uploads/2014/03/2014-03-05_13h55_46.png)
Great!

## Desmos: version 2

**Students teaching teachers:* Have one your students find this out for himself, and remark that they can enter in the entire series, but he’s having trouble finding the infinity sign. SLIDERS!*
[Link.](https://www.desmos.com/calculator/pyv84pzacp)
Whoa. (That seemed like it should be much harder to type in. Took me 5 minutes to type in the original latex code at the beginning of this post. Took me < 1 minute to actually enter the series into desmos. I had to help 1 student out of 15. That’s it. Wow easy.)
[![2014-03-05_13h58_56](http://photo180.recursiveprocess.com/wp-content/uploads/2014/03/2014-03-05_13h58_56-1024x334.png)](https://www.desmos.com/calculator/pyv84pzacp)

# Watch the power series create sin(x) step by step by moving a slider. LIVE!

We live in good times.

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