Calculus of a Single Variable, Chapter 9, 9.3, Section 9.3, Problem 78

sum_(n=1)^oo(1/n^2-1/n^3)
Apply the series sum/difference rule:
=sum_(n=1)^oo1/n^2-sum_(n=1)^oo1/n^3
Observe that both the series are p-series of the formsum_(n=1)^oo1/n^p
Recall that the p-series test is applicable for the series of the form sum_(n=1)^oo1/n^p ,where p>0
If p>1 , then the p-series converges
If 0Now, both the series have p>1
As per the p-series test , both the series converge and so their sum/difference will also converge.
Hence the series sum_(n=1)^oo(1/n^2-1/n^3) converges.