Difference between revisions of "009C Sample Final 1, Problem 2"

Revision as of 22:00, 1 February 2016

Find the sum of the following series:

a) $\sum _{n=0}^{\infty }(-2)^{n}e^{-n}$

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

Foundations:

Solution:

(a)

(b)

Step 2:

Step 3:

Final Answer:
(a)
(b)

@@ Line 1: / Line 1: @@
 <span class="exam"> Find the sum of the following series:
-::<span class="exam">a) <math>\sum_{n=0}^{\infty} (-2)^ne^{-n}</math>
+<span class="exam">a) <math>\sum_{n=0}^{\infty} (-2)^ne^{-n}</math>
-::<span class="exam">b) <math>\sum_{n=1}^{\infty} \bigg(\frac{1}{2^n}-\frac{1}{2^{n+1}}\bigg)</math>
+<span class="exam">b) <math>\sum_{n=1}^{\infty} \bigg(\frac{1}{2^n}-\frac{1}{2^{n+1}}\bigg)</math>
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 {| class="mw-collapsible mw-collapsed" style = "text-align:left;"
 !Step 3: &nbsp;
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-|-
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-'''(c)'''
-{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
-!Step 1: &nbsp;
-|-
-|
-|-
-|
-|}
-{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
-!Step 2: &nbsp;
-|-
-|
 |-
 |
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 |-
 |'''(b)'''
-|-
-|'''(c)'''
 |}
 [[009C_Sample_Final_1|'''<u>Return to Sample Exam</u>''']]