resolve 1/r(r+1) into partial fraction

Answer 1

1/(r(r+1)) = A/r + B/(r+1)
A(r+1) + Br = 1
(A+B)r + A = 1
so A = 1
A+B = 0 ==> B = -1
1/(r(r+1)) = 1/r - 1/(r+1)