Problem

Show that if $ p $ is an $ n $th-degree polynomia…

02:57

Problem 80 Hard Difficulty

Find the sum of the series.

$$ \frac {1}{1 \cdot 2} - \frac {1}{3 \cdot 2^3} + \frac {1}{5 \cdot 2^5} - \frac {1}{7 \cdot 2^7} + \cdot \cdot \cdot $$

Name: find the sum of the series frac 11 cdot 2 frac 13 cdot 23 frac 15 cdot 25 frac 17 cdot 27 cdot cdot
Uploaded: 2018-03-08
Duration: 1 min 23 s
Channel: Numerade
Description: Find the sum of the series. $$ \frac {1}{1 \cdot 2} - \frac {1}{3 \cdot 2^3} + \frac {1}{5 \cdot 2^5} - \frac {1}{7 \cdot 2^7} + \cdot \cdot \cdot $$

Answer

$\arctan\left(\frac{1}{2}\right)$

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. So fun that some of the Siri's and the missus tickle too Sigma One half to the power of two and minus one over two months one and ends from once You infinity It looks. It looks very similar to one of our familiar tear Siri's Which one's that's. We can recall that our attendant X equals two x minus X cube over three plus extra power five or five and ah so Ong and equals two extra car too. And once one over two months, one times not you want to. The power of money is all here with you have that you wanted out minus one yet So it is just park attendant one half moose.

Yiming Z.

University of Illinois at Urbana-Champaign

Topics

Sequences

Series

Calculus: Early Transcendentals

Chapter 11

Infinite Sequences and Series

Section 10

Taylor and Maclaurin Series

Problem

Show that if $ p $ is an $ n $th-degree polynomia…

Problem 80 Hard Difficulty

Find the sum of the series.

$$ \frac {1}{1 \cdot 2} - \frac {1}{3 \cdot 2^3} + \frac {1}{5 \cdot 2^5} - \frac {1}{7 \cdot 2^7} + \cdot \cdot \cdot $$

Answer

$\arctan\left(\frac{1}{2}\right)$

Topics

Calculus: Early Transcendentals

Discussion

Top Calculus 2 / BC Educators

Grace H.

Catherine R.

Heather Z.

Joseph L.

Calculus 2 / BC Bootcamp

Integration Review - Intro

Definite vs Indefinite

Recommended Videos

Watch More Solved Questions in Chapter 11

Video Transcript

Topics

Calculus: Early Transcendentals

Top Calculus 2 / BC Educators

Grace H.

Catherine R.

Heather Z.

Joseph L.

Calculus 2 / BC Bootcamp

Integration Review - Intro

Definite vs Indefinite

Recommended Videos