(adsbygoogle = window.adsbygoogle || []).push({}); [SOLVED] Convergent Series Identities

1. The problem statement, all variables and given/known data

a) If c is a number and [tex]\sum a_{n}[/tex] from n=1 to infinity is convergent to L, show that [tex]\sum ca_{n}[/tex] from n=1 to infinity is convergent to cL, using the precise definition of a sequence.

b)If [tex]\sum a_{n}[/tex] from n=1 to infinity and [tex]\sum b_{n}[/tex] from n=1 to infinity are convergent to X and Y respectively, show that [tex]\sum b_{n}+a_{n}[/tex] from n=1 to infinity is convergent to X+Y.

2. Relevant equations

I personally thought these were identities, and have no idea how to approach them.

3. The attempt at a solution

a) Maybe [tex]\sum a_{n}[/tex] from n=1 to infinity = [tex] Lim (S_{n}) [/tex] as n goes to infinity, has something to do with it

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# Homework Help: Convergent Series Identities

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