009C Sample Final 2, Problem 2

For each of the following series, find the sum if it converges. If it diverges, explain why.

a) $4-2+1-{\frac {1}{2}}+{\frac {1}{4}}-{\frac {1}{8}}+\cdots$

b) $\sum _{n=1}^{+\infty }{\frac {1}{(2n-1)(2n+1)}}$

Foundations:

Solution:

(a)

Step 1:

Step 2:

(b)

Step 1:

Step 2:

Final Answer:
(a)
(b)

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