Difference between revisions of "009C Sample Final 3, Problem 2"

Revision as of 11:42, 18 February 2017

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.

Solution:

(a)

Step 2:

(b)

Step 2:

Final Answer:
(a)
(b)

@@ Line 1: / Line 1: @@
-<span class="exam">Compute
+<span class="exam"> Consider the series
-::<span class="exam">a) <math style="vertical-align: -12px">\lim_{n\rightarrow \infty} \frac{3-2n^2}{5n^2+n+1}</math>
+::::<math>\sum_{n=2}^\infty \frac{(-1)^n}{\sqrt{n}}.</math>
-::<span class="exam">b) <math style="vertical-align: -12px">\lim_{n\rightarrow \infty} \frac{\ln n}{\ln 3n}</math>
+::<span class="exam">a) Test if the series converges absolutely. Give reasons for your answer.
+::<span class="exam">b) Test if the series converges conditionally. Give reasons for your answer.
 {| class="mw-collapsible mw-collapsed" style = "text-align:left;"