(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

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Convergent Series Identities

**Physics Forums | Science Articles, Homework Help, Discussion**