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

Revision as of 08:41, 5 February 2017

Consider the infinite series $\sum _{n=2}^{\infty }2{\bigg (}{\frac {1}{2^{n}}}-{\frac {1}{2^{n+1}}}{\bigg )}.$

a) Find an expression for the

n

th partial sum

s_{n}

of the series.

b) Compute

\lim _{n\rightarrow \infty }s_{n}.

Solution:

(a)

Step 1:

Step 2:

(b)

Final Answer:
(a)
(b)

@@ Line 1: / Line 1: @@
-<span class="exam">
+<span class="exam">Consider the infinite series <math>\sum_{n=2}^\infty 2\bigg(\frac{1}{2^n}-\frac{1}{2^{n+1}}\bigg).</math>
-::<span class="exam">a)
+::<span class="exam">a) Find an expression for the <math>n</math>th partial sum <math>s_n</math> of the series.
-::<span class="exam">b)
+::<span class="exam">b) Compute <math>\lim_{n\rightarrow \infty} s_n.</math>