Question

How do you use the ratio test to test the convergence of the series `∑(5^k+k)/(k!+3)` from n=1 to infinity?

Answer 1

See below

Explanation:

Trying to add some understanding about that series. `∑(5^k+k)/(k!+3) = sum 5^k/(k!+3) + sum 1/((k-1)!+3/k)< sum 5^k/(k!) + sum 1/((k-1)!) = e^5+e^1` so the series converges for a number `gamma` such that

`gamma < e^5+e^1`