well, applying the root test we have to compute
so the series converges, and absolutely, since it's a series with positive terms.
my friend and i are having differences on this problem .... please help
sumation of n=1 to inifinity ((n-1)/(n+1))^n(n+1)
he keeps getting that series diverges due to the divergence test
I keep getting that the series absolutely converges due to the root test
please help and show us who is right
A more highfalutan to do it is to notice that , and with a little algebraic manipulation, the RHS is equal to . Notice though that which of course implies that . So then we can see that converges by the limit comparison test with , which then means that the actual series converes by the comparison test.