Difference between revisions of "009C Sample Final 3, Problem 1"

Revision as of 17:52, 4 March 2017

Which of the following sequences $(a_{n})_{n\geq 1}$ converges? Which diverges? Give reasons for your answers!

(a) $a_{n}={\bigg (}1+{\frac {1}{2n}}{\bigg )}^{n}$

(b) $a_{n}=\cos(n\pi ){\bigg (}{\frac {1+n}{n}}{\bigg )}^{n}$

Solution:

(a)

ExpandStep 2:

(b)

ExpandStep 2:

ExpandFinal Answer:
(a)
(b)

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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 &nbsp;<math>(a_n)_{n\ge 1}</math>&nbsp; converges? Which diverges? Give reasons for your answers!
-::<span class="exam">a)&nbsp; <math>a_n=\bigg(1+\frac{1}{2n}\bigg)^n</math>
+<span class="exam">(a) &nbsp;<math>a_n=\bigg(1+\frac{1}{2n}\bigg)^n</math>
-::<span class="exam">b)&nbsp; <math>a_n=\cos(n\pi)\bigg(\frac{1+n}{n}\bigg)^n</math>
+<span class="exam">(b) &nbsp;<math>a_n=\cos(n\pi)\bigg(\frac{1+n}{n}\bigg)^n</math>
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