Solve for A and B if:
1/(k*(k+1)) = A/k + B/(k+1)
Thanks
Multiply by $\displaystyle k$: $\displaystyle \displaystyle\frac{1}{k+1}=A+\frac{Bk}{k+1}$.
Put $\displaystyle k=0$: we get $\displaystyle 1=A$
Now, multiply the first equality by $\displaystyle k+1$: $\displaystyle \displaystyle\frac{1}{k}=\frac{A(k+1)}{k}+B$.
Put $\displaystyle k=-1$: we get $\displaystyle -1=B$