# test for convergence

• Mar 31st 2009, 08:18 PM
twilightstr
test for convergence
find the sum of arcsin(1/square root n.) from n =1 to infinity.

i think arcsin(1/square root n.) is approx arcsin(1/square root n).

i tried using the limit comaprison test but it did not work for me
I think im just confused.
• Apr 1st 2009, 12:31 AM
matheagle
I don't know what ...arcsin(1/square root n.) is approx arcsin(1/square root n)... means

DIVERGENT. Limit comp to $\sum {1\over \sqrt{n}}$. Let $m={1\over \sqrt{n}}$

Then $\lim_{n\to\infty}{ {1\over \sqrt{n} }\over \arcsin {1\over \sqrt{n}}} =\lim_{m\to 0^+}{m\over \arcsin m}=\lim_{m\to 0^+}\sqrt {1-m^2}=1$.