Question

Hello, Use the divergence test to determine wheter the following series diverge or state that the test is inconclusive:

Answer 1

\[\sum_{k=2}^{\infty}\frac{ \sqrt{k} }{ \ln ^{10}k }\]

Answer 2

and one more,

\[\sum_{k=1}^{\infty}\frac{\sqrt{k ^{2}+1} }{ k }\]

Answer 3

I am stuck on how to evluate these, using the divergence test,

Answer 4

\[\lim_{k \rightarrow +\infty}\frac{ \sqrt{k ^{2}+1} }{ k }=1\] So your series diverges. You can do the same for the first one.

Answer 5

How did you get that? and I still need help with the first one.Please

Answer 6

mostly I need help wit the first series

Answer 7

\[\lim_{k \rightarrow +\infty}\frac{ \sqrt{k ^{2}+1} }{ k }=\lim_{k \rightarrow +\infty}\frac{ \sqrt{k ^{2}+1} }{ \sqrt{k ^{2}}}=\lim_{k \rightarrow +\infty}\sqrt{\frac{ k ^{2}+1 }{ k ^{2} }}= \lim_{k \rightarrow +\infty}\frac{ k ^{2} }{ k ^{2} }=1\]

Answer 8

what about the first series? can you help with that?

Answer 9

\[\lim_{k \rightarrow +\infty}\frac{ \sqrt{k} }{ \ln ^{10}k }=+\] So it diverges too.

Answer 10

+infinity*