Question

How do you test for convergence for `sum(5^k+k)/(k!+3)` from k=1 to infinity?

Answer 1

See below.

Explanation:

`sum_(k=1)^oo(5^k+k)/(k!+3) < sum_(k=1)^oo(5^k)/(k!) + sum_(k=1)^oo(k)/(k!) le e^5+e` so it converges.