Question

for each series determine if the series is absolutely convergent and convergent

the sum from 0 to infinity of (-1)^n/(the square root of (n+1))


I did the ratio test and got -1, which is less than 0 making it absolutely convergent, but do i need to take the absolute value of -1? which would then make the test inconclusive?

Answer 1

Yes, you need to take the absolute value of everything, so you get 1 which is inconclusive. If you do the integral test, you find that it diverges.