Problem

Find the sum of the series. $ \sum_{n = 0}^{\i…

01:00

Problem 73 Hard Difficulty

Find the sum of the series.

$ \sum_{n = 0}^{\infty} (-1)^n \frac {x^{4n}}{n!} $

Name: find the sum of the series sum_n 0infty 1n frac x4nn
Uploaded: 2018-03-08
Duration: 1 min 15 s
Channel: Numerade
Description: Find the sum of the series. $ \sum_{n = 0}^{\infty} (-1)^n \frac {x^{4n}}{n!} $

Answer

$e^{-x^{4}}$

Topics

Sequences

Series

Calculus: Early Transcendentals

Chapter 11

Infinite Sequences and Series

Section 10

Taylor and Maclaurin Series

Discussion

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Video Transcript

Okay, fund this Some of the Siri's s. So this is Look, this looks very similar to our exponential function. But of course, we're gonna do some, like some change wearables to make it look similar to eat a power X. So is this him too? And from zero to Philly and minus one times except for four to the powers in Over in factorial. And let's see if we change t equals not you extra port for And this is just so it is Pete to the poor tea. So it was to eat. Report, Not you. Oh four. And this is our results. Shakespeare. Nothing. That's two for four.

Yiming Z.

University of Illinois at Urbana-Champaign