To sum 1/[k(k+d)]: decompose as (1/d)[1/k - 1/(k+d)]. Examples: 1/[k(k+1)] = 1/k - 1/(k+1). 1/[k(k+2)] = (1/2)[1/k - 1/(k+2)]. 1/[k(k+3)] = (1/3)[1/k - 1/(k+3)]. For products of 3 consecutive: 1/[k(k+1)(k+2)] = (1/2)[1/(k(k+1)) - 1/((k+1)(k+2))], which telescopes after one more layer.