Calculus series problem?

Question

Determine if series is convergent or Diverget. If convergent, find sum.
∞
∑ ((3/5^n) + (2/n))
n=1

The problem is 34 in 12.2 (page 756) in Calculus Stewart 5th edition
Thanks for any help!

Answer 1

It is divergent.

Note that ((3/5^n)+(2/n)) >1/n for all positive integer n. Then since the series 1/n is divergent (the harmonic series - can be shown to diverge through the integral test), your series is then divergent by the direct comparison test.

Hope that helps!

Answer 2

divergent becuase of the 2/n part

you can prove it yourself by adding separately
1/2 1/3+1/4>2/4 1/5+1/6+1/7+1/8>4/8
every group of 2^n terms is more than 1/2 so it must diverge

Answer 3

the first summand is a term of a geometric series with r=1/5 convergent,but the second is 2(1/n) which is a term of the harmonic series divergent.So the series is divergent