Hope all of you had a good July 4th (for those that celebrate it)!(adsbygoogle = window.adsbygoogle || []).push({});

Anyways, I'm trying to figure out series and sequences. I'm using Stewarts' Single Variable Calculus: Early Transcendentals, 6th. ed.

For instance, under Section 11.4, the Comparison Tests, I don't understand how one arrives at b_{n}.

Example:

[tex]\Sigma[/tex][tex]^{\infty}_{n=1}[/tex][tex]\frac{1}{2^{n}-1}[/tex]

The book then proceeds to state:

a_{n}= [tex]\frac{1}{2^{n}-1}[/tex], which I understand because it's written as [tex]\Sigma[/tex]a_{n}.

However, the book then proceeds to state that:

b_{n}= [tex]\frac{1}{2^{n}}[/tex], which I have no idea how they got there. Do I just remove all constants from a_{n}? Or do I remove all variables that are not attached by an"n"?

Also, my Calculus 1 is a bit rusty, but how exactly does (excerpted from p.717, Example 4 of Stewarts)

[tex]\frac{(n+1)^{3}}{3^{n+1}}[/tex] [tex]\times[/tex] [tex]\frac{3^{n}}{n^{3}}[/tex]

=[tex]\frac{1}{3}[/tex]([tex]\frac{n+1}{n}[/tex])^{3}

=[tex]\frac{1}{3}[/tex](1+[tex]\frac{1}{n}[/tex])^{3}

=[tex]\frac{1}{3}[/tex]

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# Homework Help: Series and Sequences

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