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

Revision as of 20:07, 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:

(c)

Step 1:

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+<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">b) <math>\sum_{n=1}^{\infty} \bigg(\frac{1}{2^n}-\frac{1}{2^{n+1}}\bigg)</math>
 {| class="mw-collapsible mw-collapsed" style = "text-align:left;"
 !Foundations: &nbsp;