Question

观察规律:1/1*2=1-1/2;1/2*3=1/2-1/3;1/3*4=1/3-1/4.捷达下列个题

Answer 1

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

[2] ∵ 1/（1×2）+1/(2×3）+1/(3×4）+.+1/n(n+1)

=1-1/2+1/2-1/3+1/3-1/4+.+1/n - 1/(n+1)

=1-1/(n+1)

[3]原式=1-1/2015=2014/2015 【求和少了一项?1/(2014×2015）?】

证明；∵ 1-1/1×2=1-1/2

1/2×3=1/2-1/3

.

∴1/n(n+1)=1/n-1/n+1