Question

10) Using Limit Comparison Test (LCT), the following series

+00
M:
-1 + 2n5
n6 + 1
n=1​

Answer 1

Compare to the divergent series,

`\displaystyle\sum_(n=1)^\infty\frac1n`

Then by the limit comparison test, the given series also diverges, since the limit

`\displaystyle\lim_(n\to\infty)((2n^5-1)/(n^6+1))/(\frac1n) = \lim_(n\to\infty)(2n^6-n)/(n^6+1)=\lim_(n\to\infty)\frac{2-\frac1{n^5}}{1+\frac1{n^6}}=2`

is positive and finite.