Chapter 9.4, Problem 46E

Comparing Series It appears that the series

$\frac{1}{1000}+\frac{1}{1001}+\frac{1}{1002}+\frac{1}{1003}+\cdots$

are less than the corresponding term of the convergent series

$1+\frac{1}{4}+\frac{1}{9}+\frac{1}{16}+\cdots$

If the statement above is correct then the first series converges. Is this correct? Why or Why not?

Make a statement about how the divergence or convergence of a series is affected by the inclusion or exclusion of the first finite number of terms.