2/(2+n)^1/2 (from zero to infinity) converge or diverge? and how?

Question

perl · Answer

is this a series

anonymous · Answer

$$
\sum_1^\infty \frac 1 {n^p}
$$
diverges if  $ p\le1$ and converges if p>1

anonymous · Answer

Your series is similar to the series I mentioned with p=1/2, so it diverges

anonymous · Answer

how does it similiar?

anonymous · Answer

n and 2+n are almost the same near infinity

anonymous · Answer

Use the limit comparison test

anonymous · Answer

how

anonymous · Answer

Do you know the limit comparison test?

anonymous · Answer

ı guess ı will take limits of both sides right?

anonymous · Answer

Read this link http://math.oregonstate.edu/home/programs/undergrad/CalculusQuestStudyGuides/SandS/SeriesTests/limit_comparison.html

anonymous · Answer

ok thanks a lot

anonymous · Answer

Read the link above and things will be clearer

anonymous · Answer

YW

anonymous · Answer

may ı ask a question? could ı think it like this? : 2. 1/(n+2)^1/2 than say the 1/2 is smaller than 1 so it diverges??

anonymous · Answer

$$
\lim_{n\to \infty} \frac{2 { (n+2)^{1/2}}

}

{\frac 1 {n^{1/2}}}=2 >0
$$
So your series behaves like
$$
\sum_{n=1^{\infty}}\frac 1 {n^{1/2}}
$$
which is divergent

anonymous · Answer

Typo
$$
\sum_{n=1}^\infty\frac 1 {n^{1/2}}
$$