Difference between revisions of "009C Sample Final 3, Problem 1"
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Kayla Murray (talk | contribs) (Created page with "<span class="exam">Compute ::<span class="exam">a) <math style="vertical-align: -12px">\lim_{n\rightarrow \infty} \frac{3-2n^2}{5n^2+n+1}</math> ::<span class="exam">b) <mat...") |
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| − | <span class="exam"> | + | <span class="exam"> Which of the following sequences <math>(a_n)_{n\ge 1}</math> converges? Which diverges? Give reasons for your answers! |
| − | ::<span class="exam">a) <math | + | ::<span class="exam">a) <math>a_n=\bigg(1+\frac{1}{2n}\bigg)^n</math> |
| − | ::<span class="exam">b) <math | + | ::<span class="exam">b) <math>a_n=\cos(n\pi)\bigg(\frac{1+n}{n}\bigg)^n</math> |
{| class="mw-collapsible mw-collapsed" style = "text-align:left;" | {| class="mw-collapsible mw-collapsed" style = "text-align:left;" | ||
Revision as of 10:39, 18 February 2017
Which of the following sequences converges? Which diverges? Give reasons for your answers!
- 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 a_n=\bigg(1+\frac{1}{2n}\bigg)^n}
- b) 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 a_n=\cos(n\pi)\bigg(\frac{1+n}{n}\bigg)^n}
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Solution:
(a)
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(b)
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| Final Answer: |
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| (a) |
| (b) |