证明：对任意的正整数n,有1/1×3+1/2×4+1/3×5+.+1/n(n+2)

Question

证明：对任意的正整数n,有1/1×3+1/2×4+1/3×5+.+1/n(n+2)

Answer 1

原式=1/2[1-1/3+1/2-1/4+1/3-1/5+.+1/n-1/(n+2)]
=1/2[1+1/2-1/n-1/(n+2)]
=3/4-1/n-1/(n+2)