Question

For what values of p is each series convergent? sum from n=1 to infinity of ((-1)^n)/(n+p)

Answer 1

$$\sum_{n=1}^\infty \frac{(-1)^n}{n+p}$$
will converge as long as \(n+p>1\implies p>1-n\)

Answer 2

but sine n stars from "1"
you can say \(p>0\)

Answer 3

so is p>0 where it is convergent?
my book says p is not a negative integer as the answer. This is the same right?

Answer 4

which is what p>0 means....
but I forgot to include "0"

so, the solution set is,
\(p\ge0\)

Answer 5

thank you for your help!