Question

Determine whether the series converges or diverges
1. Sum of (2k-1)(k^2-1)/(k+1)((k^2+4)^2) with k=1 -> infinite
2. Sum of sqrt(n)/(n-1) with n=2 -> infinite
3. Sum of 1/(2n+3) with n=1 -> infinite
4. Sum of (n+2)/((n+1)^3) with n=3 -> infinite