Infinite Series Activity
In this project you will use a calculator or computer to explore the relationship of partial sums and sums of infinite series.
Consider the series
and its partial sums
1.
Calculate
2. Do these partial sums seem to be approaching any specific value in the limit? If so, what is this value?
3.
Use your
partial sums to estimate the value of
Now consider the alternating series
and its partial sums
4.
Calculate
5. Do these partial sums seem to be approaching any specific value in the limit? If so, what is this value?
6. Use your partial sums to estimate the value of the alternating series.
7.
How do the
partial sums
8.
How do the
partial sums
9. Do your observations for the last two questions apply to all alternating series? Check the theorems and proofs in your calculus textbook.