This question is from my exam paper which i had appeared last semister i am trying to solve this but dont know the right answer.
Q: Test the convergence of the series
∞
∑ 3n/2(n+1)
n=1
Please replies with explanation if possible .......
There is probably one that is a little easier to use, but you can use the integral test here:
Let . Thus,
Thus, the integral becomes
This gives us
Thus, this diverges by the integral test.
-------------------------------------------------------------------------
I just thought of an easier way to do this...
You can show that the series is divergent by the nth term test (also called Divergence Test):
. Thus, the series diverges.