quick question.. Does this series converge?

[Xtokalon]

take a series going from n = 1 out to infinity with An =

1/((n)*(n+1)*(n+2))^1/3

is the series convergent?

i tried comparison tests on this sucka but they don't work (using a p series with p = 1). what do you suggest? i'm supposing an integral test via partial fractions would do it (after a few algebraic manipulations) but there's got to be simpler solutions!

 

[capeda]

Whatever the term is for when the equation goes to zero as n goes to infinity. Just expand the denominator and look at the biggest factor (n^3)^1/3. If I'm visualizing my algebra right (I haven't taken math since I finished Calculus three years ago!), the equation will look like y=1/n as the numbers get larger.

 

[Xtokalon]

Whatever the term is for when the equation goes to zero as n goes to infinity. Just expand the denominator and look at the biggest factor (n^3)^1/3. If I'm visualizing my algebra right (I haven't taken math since I finished Calculus three years ago!), the equation will look like y=1/n as the numbers get larger.

the limit of that equation as it goes out to infinity is 0, but we can't determine from that if it's convergent or divergent.

1/1/((n)*(n+1)*(n+2))^1/3 is less than 1/n on n from [1, infinity], and we know that 1/n is a divergent harmonic series... but again this bit of information isn't telling us much. i did a limit comparison test and same deal. there's nothing going on here. we can integrate with f(x) = An, but then that's seems awfully tedious for a relatively simple polynomial ratio. i'll try to get a groove on and see if i can solve this without recoursing to integration.

sayin.