Comparing Series It appears that the terms of the series are less than the corresponding

Chapter 9, Problem 46

(choose chapter or problem)

Comparing Series It appears that the terms of the series

\(\frac{1}{1000}+\frac{1}{1001}+\frac{1}{1002}+\frac{1}{1003}+\cdots\)

are less than the corresponding terms 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.

Text Transcription:

1/1000+1/1001+1/1002+1/1003+...

1+1/4+1/9+1/16+...