Can someone give me a hint that the summation of (-1)^(u)*(u^(1/2))/(u+1) from u=1 to N is divergent, conditionally convergent, or absolutely convergent? By the looks of it it is conditionally convergent as it's absolute value diverges, but i know 1/u^(1/2)*(-1)^(u) converges and the one doesn't really matter, but I can't prove that it doesn't matter.
Thanks for the help in advance
Hello, jarny!
You've already worked out the answer . . .
It is a convergent alternating series. .(The term approaches zero.). Divergent, conditionally convergent, or absolutely convergent?
It is not absolutely convergent because: . . . . a divergent -series.
Therefore, the series is conditionally convergent.
Somehow I managed to mis-write it. It in the denominator is should be 4 instead of 1. Sorry :/ Soroban, I can see that it is approximately but I need to kind of prove it.
when its (-1)^(u) *(u)^(1/2)/(u+4) could I just find a particular u (in this case 4) where the absolute value of the series begins to decrease and say since a_1>a_2>a_3 ...>a_N and since the lim n->infinity is zero (and the summands before 4 are finite) that by the alternating series test the summation is conditionally convergent?