Question

Does this sum converge? n=1 to infinity of (1/3^n) - (5/sqrt(n))

Answer 1

\[\sum_{1}^{\infty} \frac{ 1 }{ 3^n }-\frac{ 5 }{ \sqrt{n} }\] is this the problem?

Answer 2

yes

Answer 3

sum (1/n) diverges
i/sqrt(n) = sqrt(n)/n > 1/n
so sum(1/sqrt(n)) diverges, and the whole expression will.