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

Revision as of 10:39, 18 February 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)

Step 2:

(b)

Step 2:

Final Answer:
(a)
(b)

@@ Line 1: / Line 1: @@
-<span class="exam">Compute
+<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 style="vertical-align: -12px">\lim_{n\rightarrow \infty} \frac{3-2n^2}{5n^2+n+1}</math>
+::<span class="exam">a)&nbsp; <math>a_n=\bigg(1+\frac{1}{2n}\bigg)^n</math>
-::<span class="exam">b) <math style="vertical-align: -12px">\lim_{n\rightarrow \infty} \frac{\ln n}{\ln 3n}</math>
+::<span class="exam">b)&nbsp; <math>a_n=\cos(n\pi)\bigg(\frac{1+n}{n}\bigg)^n</math>
 {| class="mw-collapsible mw-collapsed" style = "text-align:left;"