Consider the series the sum of x^-n for values of n from 1 to infinity.

Looks kinda like that:

infinity

sigma x^-n.

n=1

a) What is the interval of convergence?

b) In terms of x, find the sum of the series.

I have no idea how to find the interval of convergence

I tried making charts where x =1 and I'd go

n = 1, x^-n = 1

n = 2, x^-n = 1/1^2 = 1

n = 3, x^-n = 1/1^3 = 1

....

...

and then x = 2

n = 1, x^-n = 1/2

n = 2, x^-n = 1/2^2 = 1/4

n = 3, x^-n = 1/2^3 = 1/8

...

...

I'm assuming the interval of convergence is when my outputs start becoming positive and negative. (ex: -1, 2, -3, 4...)

Then for B, I tried using the sequence formula of adding the sum of an infinite geometric sequence.

I did: Sn = T1 / 1-r

= X^-1 / 1-(-n)

= 1/x / 1+n

= 1/x * 1+n/1 = 1+n / x

Help would be greatly appreciated, thank you!

~Wingless