1/(n+1)(n+2)=1/(n+1)-1/(n+2)

The partial sum Sₖ of the series being of the form ᵏ⅀ₙ₌₀{f(n) - f(n + 1)} = f0) - f(k + 1) where f(r) = 1/(r + 1), as k →∞, Sₖ → f(0) = 1.