Question

Convergent or Divergent?
.....

Answer 1

\[\sum_{n=1}^{\infty} = (1/n)/(\ln(n)\sqrt{\ln^2(n)-1})\]

Answer 2

If limit n tending to infinity exist then series is convergent else divergent

Answer 3

The series is convergent

Answer 4

Is the 2nd derivative test necessary in this problem to determine if its decreasing?

Answer 5

is this a function or a sum of the series whose convergence has to be determined

Answer 6

Its a series

Answer 7

I determined sum to infinty is a finite number hence it is convergent
Else
U can assume it to be a function of integer variable and take first derivative and show it to be decreasing and also at n=1 it has finite value then it is converging

Answer 8

cool, thanks a lot.