009C Sample Final 3, Problem 2

Consider the series

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

a) Test if the series converges absolutely. Give reasons for your answer.

b) Test if the series converges conditionally. Give reasons for your answer.

Foundations:

Solution:

(a)

Step 1:

Step 2:

(b)

Step 1:

Step 2:

Final Answer:
(a)
(b)

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