1\2+1\6+1\12+.+n（n+1）等于多少啊

网友回答

因为：1/[n(n+1)]=1/n-1/(n+1)
所以：1/2+1/6+1/12+……+1/[n(n+1)]
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+…+[(1/n-1/(n+1)]
=1-1/2+1/2-1/3+1/3……-1/(n+1)
=1-1/(n+1)
=(n+1)/(n+1)-1/(n+1)
=n/(n+1)
======以下答案可供参考======
供参考答案1:
有才供参考答案2:
1/2+1/6+1/12+...+1/n(n+1)
=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)
=n/(n+1)