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.

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- Mar 31st 2009, 07:18 PMtwilightstrtest 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. - Mar 31st 2009, 11:31 PMmatheagle
I don't know what ...arcsin(1/square root n.) is approx arcsin(1/square root n)... means

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

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