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

Latest revision as of 18:22, 2 December 2017

For each of the following series, find the sum if it converges. If it diverges, explain why.

(a) Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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

Detailed Solution

Return to Sample Exam

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 <span class="exam">(a) &nbsp;<math style="vertical-align: -14px">4-2+1-\frac{1}{2}+\frac{1}{4}-\frac{1}{8}+\cdots</math>
-<span class="exam">(b) &nbsp;<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;"
+<hr>
-!Foundations: &nbsp;
+[[009C Sample Final 2, Problem 2 Solution|'''<u>Solution</u>''']]
-|-
-|'''1.''' The sum of a convergent geometric series is &nbsp; <math>\frac{a}{1-r}</math>
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-|&nbsp; &nbsp; &nbsp; &nbsp; where &nbsp;<math style="vertical-align: 0px">r</math>&nbsp; is the ratio of the geometric series
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-|&nbsp; &nbsp; &nbsp; &nbsp; and &nbsp;<math style="vertical-align: 0px">a</math>&nbsp; is the first term of the series.
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-|'''2.''' The &nbsp;<math style="vertical-align: 0px">n</math>th partial sum, &nbsp;<math style="vertical-align: -3px">s_n</math>&nbsp; for a series &nbsp;<math>\sum_{n=1}^\infty a_n </math>&nbsp; is defined as
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-&nbsp; &nbsp; &nbsp; &nbsp; <math>s_n=\sum_{i=1}^n a_i.</math>
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-'''Solution:'''
+[[009C Sample Final 2, Problem 2 Detailed Solution|'''<u>Detailed Solution</u>''']]
-'''(a)'''
-{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
-!Step 1: &nbsp;
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-{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
-!Step 2: &nbsp;
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-'''(b)'''
-{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
-!Step 1: &nbsp;
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-{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
-!Step 2: &nbsp;
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-{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
-!Final Answer: &nbsp;
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-|&nbsp;&nbsp; '''(a)'''
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-|&nbsp;&nbsp; '''(b)'''
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 [[009C_Sample_Final_2|'''<u>Return to Sample Exam</u>''']]

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

Latest revision as of 18:22, 2 December 2017

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