If (a+b):(a-b) = 1:5, then (a^2 - b^2):(a^2 + b^2) equals to what ?

Question

If
1^2 + 2^2 + 3^2 + ................. 100^2 = A &
1^3 + 2^3 + 3^3 + .................. 100^3 = B
Then
1^2*2 + 2^2*3 + 3^2*4 + 4^2*5 ........ 99^2*100 + 100^2*101=??

Answer 1

(4/9) / (13/9) = 0.386
(a + b) / (a - b) = 1/5
5a + 5b = a - b
b = -4/6 * a
.
a^2 = a^2
b^2 = (-4/6 * a)^2 = (-4/6)^2 * (a)^2 = 4/9 * a^2
.
(a^2 - b^2) / (a^2 + b^2) =
(a^2 - 4/9 * a^2) / (a^2 + 4/9 a^2) =
(5/9 * a^2) / (13/9 * a^2) = (5/9) / (13/9)

Answer 2

a+b / a-b = 1/5
a+b+a-b / a+b-a+b = 1+5 / 1-5
a/b = - 3/2

a^2 / b^2 = 9/4
a^2 - b^2 / a^2 + b^2 = 9-4 / 9+4 = 5/13