1/(1*2)+1/(2*3)+1/(3*4)+……+1/(98*99)+1/99*100
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1/(1*2)+1/(2*3)+1/(3*4)+……+1/(98*99)+1/99*100
1/(1*2)+1/(2*3)+1/(3*4)+……+1/(98*99)+1/99*100
1/(1*2)+1/(2*3)+1/(3*4)+……+1/(98*99)+1/99*100
1/1X2,可以化简为1-1/2
同样道理,1/2X3化简为1/2-1/3
之后一直化到最后
你会发现中间项全被抵消了
只剩下1-1/100=99/100
1/1*2+1/2*3+1/3*4+1/4*5+...+1/99*100
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)......+(1/99-1/100)
前面括号的后一项与后面括号的前一项正好抵消
=1- 1/100
=99/100
1/(1*2)+1/(2*3)+1/(3*4)+……+1/(98*99)+1/99*100
=1-1/2+1/2-1/3+1/3-1/4+....+1/99-1/100
=1-1/100
=99/100
1/1*2=1-1/2
1/2*3=1/2-1/3
……………………
……………………
1/99*100=1/99-1/100
上面式子相加就可以了。
1/(1*2)=1/1-1/2
1/(2*3)=1/2-1/3
同理
原式=1/1-1/2+1/2-/-1/3+1/3……-1/100
=99/100
原式=(1/1-1/2)+(1/2-1/3)+(1/3-1/4)……+(1/98-1/99)+(1/99-1/100)
然后展开发现中间的东西一加一减都没了
最后原式=1/1-1/100=99/100
这个规律一直到你高中都会用,一定要记住啊!
1/(1*2)+1/(2*3)+1/(3*4)+……+1/(98*99)+1/99*100
=1-1/2+1/2-1/3+1/3-1/4+....+1/99-1/100
=1-1/100
=99/100
1/1*2=1-1/2
1/2*3=1/2-1/3
……………………
……………………
1/99*100=1/99-...
全部展开
1/(1*2)+1/(2*3)+1/(3*4)+……+1/(98*99)+1/99*100
=1-1/2+1/2-1/3+1/3-1/4+....+1/99-1/100
=1-1/100
=99/100
1/1*2=1-1/2
1/2*3=1/2-1/3
……………………
……………………
1/99*100=1/99-1/100
上面式子相加就可以了。
原式=(1/1-1/2)+(1/2-1/3)+(1/3-1/4)……+(1/98-1/99)+(1/99-1/100)
然后展开发现中间的东西一加一减都没了
最后原式=1/1-1/100=99/100
这个规律一直到你高中都会用,一定要记住啊!
收起
答案:99/100
理由:1/(1*2)=1-1/2
1/(2*3)=1/2-1/3
1/(3*4)=1/3-1/4
.
.
.
∴1/(1*2)+1/(2*3)+1/(3*4)+……+1/(98*99)+1/99*100
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+…...
全部展开
答案:99/100
理由:1/(1*2)=1-1/2
1/(2*3)=1/2-1/3
1/(3*4)=1/3-1/4
.
.
.
∴1/(1*2)+1/(2*3)+1/(3*4)+……+1/(98*99)+1/99*100
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+……+(1/98-1/99)+(1/99-1/100) =1-1/2+1/2-1/3+1/3-1/4+……+1/98-1/99+1/99-1/100
=1-1/100
=99/100
收起
1/(1*2)+1/(2*3)+1/(3*4)+……+1/(98*99)+1/99*100
=1-1/2+1/2-1/3+1/3-1/4+....+1/99-1/100
=1-1/100
=99/100
1/(1*2)+1/(2*3)+1/(3*4)+……+1/(98*99)+1/99*100
=1-1/2+1/2-1/3+1/3-1/4+....+1/99-1/100
=1-1/100
=99/100
99/100