Using the comparison test, how do I find the divergence of the series below?

Question

infinity

Σk=1 (1+1/k)^k

Answer 1

The limit of (1+1/k)^k as k goes to infinity is e. This is a constant limit which means that each term adds a value closer and closer to e. A constant value for the terms will not allow the series to converge (The terms must decrease in order to converge). You could do the limit test with the constant e as in ∑(k =1, ∞) e, which, does not converge, but has the same limiting behavior as your series.

Hope that helps.