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

Latest revision as of 22:52, 11 November 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 $\lim _{n\rightarrow \infty }s_{n}.$

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-<span class="exam">
+<span class="exam">Consider the infinite series &nbsp;<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 &nbsp;<math style="vertical-align: 0px">n</math>th partial sum &nbsp;<math style="vertical-align: -3px">s_n</math>&nbsp; of the series.
-::<span class="exam">b)
+<span class="exam">(b) Compute &nbsp;<math style="vertical-align: -11px">\lim_{n\rightarrow \infty} s_n.</math>
+<hr>
+[[009C Sample Midterm 1, Problem 2 Solution|'''<u>Solution</u>''']]
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+[[009C Sample Midterm 1, Problem 2 Detailed Solution|'''<u>Detailed Solution</u>''']]
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 [[009C_Sample_Midterm_1|'''<u>Return to Sample Exam</u>''']]