Difference between revisions of "009C Sample Final 2, Problem 1"

Revision as of 11:08, 18 February 2017

Test if the following sequences converge or diverge. Also find the limit of each convergent sequence.

a)

a_{n}={\frac {\ln(n)}{\ln(n+1)}}

b)

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

Solution:

(a)

Step 2:

(b)

Step 2:

Final Answer:
(a)
(b)

@@ Line 1: / Line 1: @@
-<span class="exam">Compute
+<span class="exam">Test if the following sequences converge or diverge. Also find the limit of each convergent sequence.
-::<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) <math style="vertical-align: -12px">a_n=\frac{\ln(n)}{\ln(n+1)}</math>
-::<span class="exam">b) <math style="vertical-align: -12px">\lim_{n\rightarrow \infty} \frac{\ln n}{\ln 3n}</math>
+::<span class="exam">b) <math style="vertical-align: -12px">a_n=\bigg(\frac{n}{n+1}\bigg)^n</math>
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