Thread: Series convergance?

does these series conv. or diver.?

1. to infiity n=1
im not sure where to start exactly, i was thinking Ratio or root test but im lost

2. to infinity n=1
same as above, not sure


any help/tips would be greatly appreciated

Thanks

1. arctan(n)<pi/2

So use comparison test with the conv pseries 1/n^3

2. rewrite (-3/4)^n - (1/4)^n the sum of 2 convergent geometric series

Originally Posted by Itsygo

does these series conv. or diver.?

1. to infiity n=1
im not sure where to start exactly, i was thinking Ratio or root test but im lost

2. to infinity n=1
same as above, not sure


any help/tips would be greatly appreciated

Thanks

I'll have a think about these, but for 1., I would say you could use a comparison test (could someone verify?)

Since we can say that

, which is a p-series.

This p-series converges to a number, and since the original series is less than this number, the original series must also converge.