Question

求 简算1 1 1 1—――—― ＋ ――—― ＋ —――—― ＋ ……… ＋ —――—――1×2×3 2 ×3×4 3

Answer 1

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

所以原式=1/2(1+1/2-1/21-1/22)=115/462