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

Revision as of 17:39, 4 March 2017

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

Solution:

(a)

Step 2:

(b)

Step 2:

Final Answer:
(a)
(b)

@@ Line 1: / Line 1: @@
 <span class="exam"> For each of the following series, find the sum if it converges. If it diverges, explain why.
-::<span class="exam">a) <math>4-2+1-\frac{1}{2}+\frac{1}{4}-\frac{1}{8}+\cdots</math>
+<span class="exam">(a) &nbsp;<math>4-2+1-\frac{1}{2}+\frac{1}{4}-\frac{1}{8}+\cdots</math>
-::<span class="exam">b) <math>\sum_{n=1}^{+\infty} \frac{1}{(2n-1)(2n+1)}</math>
+<span class="exam">(b) &nbsp;<math>\sum_{n=1}^{+\infty} \frac{1}{(2n-1)(2n+1)}</math>
 {| class="mw-collapsible mw-collapsed" style = "text-align:left;"