Hey bakinbacon.
You need to consider the integral which should be [(1/2)arctan(x/2)] {x=1,x=infinity} and show that the answer is finite and if so then the series converges by the integral test.
If it doesn't converge then the series will diverge.
I have to use the integral test to figure out if the summation of 1/(n^{2}+4) converges or diverges.
the first thing I did was set it to a function (1/(x^{2}+4)) then I set up an integral from 1 to infinity for that function. Then took the limit as b>infinity from 1 to b for f(x).
I'm stuck here. The solution manual says that I should get the following:
lim as b>inf [(1/2)Tan^{-1}(x/2)] from b to 1.
Can someone explain this to me please? I can figure out the steps after but I don't understand this step.
Hey bakinbacon.
You need to consider the integral which should be [(1/2)arctan(x/2)] {x=1,x=infinity} and show that the answer is finite and if so then the series converges by the integral test.
If it doesn't converge then the series will diverge.