Question

determine whether series diverges or converges

Answer 1

I believe limit compassion test will do the job

Answer 2

yes @sourwing but I'm having trouble working it out

Answer 3

just compare with 1/k. The trick is that, since k is positive, 1/k = 1/sqrt(k^2)

Answer 4

so you have 1/sqrt(k(k+1)) divides 1/sqrt(k^2). Then take the limit

Answer 5

I believe the limit is 1, which is finite and positive. And since 1/k is divergent, the original series is also divergent

Answer 6

wow thank you! let me see if i am able to work it through!

Answer 7

@sourwing I got it :)

Answer 8

I don't think that will work since 1/k is larger than 1/sqrt(k(k+1))

Answer 9

the test was "Limit" Comparison test, not Comparison test.

Answer 10

See if they were the other way around, then you could show that it converges.