# Series Identities

## Homework Statement

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

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

## Homework Equations

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

## The Attempt at a Solution

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

I cross posted this in Calculus & Beyond and Pre-Calculus because I wasn't sure where it belongs

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