Question

Find the radius of convergence, R, of the series.

∞
n = 1

(−1)ⁿxⁿ

n²

R = ?

Find the interval, I, of convergence of the series. (Enter your answer using interval notation.)

I = ?

Answer 1

we have

so,

by the ratio test,

we know that |-1|=1

L < 1 for the series is convergence,

the radius of the convergence R = 1

the given series is converges at both end,

hence the interval of the convergence,