009C Sample Final 3, Problem 4

Determine if the following series converges or diverges. Please give your reason(s).

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

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

Foundations:

Solution:

(a)

Step 1:

Step 2:

(b)

Step 1:

Step 2:

Final Answer:
(a)
(b)

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