Question

Use the RATIO test to determine whether the series is convergent or divergent.

a) sigma from n=1 to infinity of (1/n!)

b) sigma from n=1 to infinity of (2n)!/(3ⁿ)

Use the ROOT test to determine whether the series converges or diverges.

a) sigma from n=1 to infinity of    (tan^-1(n))^-n

b) sigma from n=1 to infinity of ((-2n)/(n+1))⁵ⁿ

For each series, use and state any appropriate tests to decide if it converges or diverges. Be sure to verify all necessary conditions for the tests you use, state your conclusion, and clearly show all work.

a)sigma from n=1 to infinity of eⁿ/n²

b) sigma from n=1 to infinity of n/sqrt(n⁵+n+1)

Answer 1