Question

1/2+1/6+1/12+1/20+.+1/90的答案是多少

Answer 1

1/2+1/6+1/12+1/20+...+1/90
=1/(1×2)+1/(2×3)+1/(3×4)+1/(4×5)+...+1/(9×10)
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+...+1/9-1/10
=1- 1/10
=9/10

总结：
1、本题是拆项法的典型习题。
2、拆项方法：1/[n(n+1)]=1/n -1/(n+1)
3、推广到一般情况：
1/2+1/6+...+1/[n(n+1)]
=1/(1×2)+1/(2×3)+...+1/[n(n+1)]
=1-1/2+1/2-1/3+...+1/n-1/(n+1)
=1- 1/(n+1)
=n/(n+1)

Answer 2

答：题目可以化简为：
1+（1/2-1/3）+(1/3-1/4)+(1/4-1/5)+...+(1/9-1/10)
=1+1/2-1/10
= 7/5

望采纳

Answer 3

解答过程如下：
1/2+1/6+1/12+1/20+1/30+.+1/72+1/90
= 1/1*2 +1/2*3 +1/3*4 +...+1/8*9 +1/9*10
= (1/1 -1/2)+(1/2 -1/3)+...+(1/8 -1/9)+(1/9 -1/10)
= 1/1 -1/10
= 9/10