- #1

Brilliant

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## Homework Statement

If [tex]\sum_{n=0}^{\infty} c_{n}4^n[/tex] is convergent, does it follow that the following series are convergent?

a) [tex]\sum_{n=0}^{\infty} c_{n}(-2)^n[/tex] b) [tex]\sum_{n=0}^{\infty} c_{n}(-4)^n[/tex]

## Homework Equations

The Power Series: [tex]\sum_{n=0}^{\infty} c_{n}(x - a)^n[/tex]

## The Attempt at a Solution

I was able to work all the problems that asked me to solve for a radius of convergence, but this question seems much different, and I can't think about how to prove or disprove either a or b. Any tips would be much appreciated.