1/2+1/6+1/12+1/20+···+1/n(n+1)的值为（），其中n为自然数

1/2+1/6+1/12+1/20+...+1/n(n+1)
=(1-1/2) + (1/2-1/3) + (1/3-1/4) + (1/4-1/5) +...+ (1/n-1/(n+1))
=1-1/(n+1)
=n/(n+1)

1/6=1/2-1/3 1/12=1/3-1/4 ...
类推可得 结果是n/n+1

当n趋向于无穷大时等于1,

否则等于1-1/(n+1)

高中的题？？？

1/2+1/6+1/12+1/20+···+1/n(n+1)
=(1/1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+...+(1/n-1/(n+1))
=1-1/(n+1)
极限是1

1/2+1/6+1/12+1/20+···+1/n(n+1)
=1/2 + (1/2 - 1/3) + (1/3 - 1/4) + (1/4 + 1/5) + ......(1/(n-1) -1/n) + (1/n - 1/(n+1))
=1 - 1/(n+1)