Question

interval of convergence

Answer 1

(-2,8]

Answer 2

@Valpey that was for the last question.

Answer 3

You can write \infty for the infinity symbol in LaTeX.

Answer 4

oh thanks for the tip didnt know you could do that

Answer 5

\[\sum_{n=0}^{\infty}\frac{(-1)^n}{2^n}x^n\]Ratio Test:\[\large \frac{\frac{(-1)^{n+1}}{2^{n+1}}x^{n+1}}{\frac{(-1)^{n}}{2^{n}}x^{n}}=\frac{-1}{2}x\]Will converge for x where |-1/2x|<1, right?

Answer 6

Yeah so that makes the values of x from -2 to 2 right?

Answer 7

It definitely diverges at x=-2; At x=2 we have an expanding alternating series which diverges.

Answer 8

I realize I omitted the n from the numerator.

Answer 9

but once you do lhopital it goes away anyways