Find ∑(j=12 up to 99) of

Question

2j+1/(((j+1)^2)j^2)

Answer 1

(2j+1) / (j+1)^2 j^2 ???

(2j+1) / (j^2 + 2 j + 1)j^2

(2 j + 1) / (j^4 + 2 j^3 + j^2)

(2 j + 1) / (j^2 + 2 j^3 + j^4)

try 12
25/( 144 + 3456 + 20736)= 25/24336
= .001027
this is going to get small fast
the denominator will be totally dominated by j^4
and what we really will have is

sum from say j = 13 to j = 99 of
2/j^3