Difference between revisions of "009C Sample Final 3, Problem 1"
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| − | <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"> 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>a_n=\bigg(1+\frac{1}{2n}\bigg)^n</math> | |
| − | + | <span class="exam">(b) <math>a_n=\cos(n\pi)\bigg(\frac{1+n}{n}\bigg)^n</math> | |
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Revision as of 16:52, 4 March 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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| (a) |
| (b) |