计算:3/2-5/6+7/12-9/20+…-197/9702+199/9900(提示:3/2=1+2/1*2,5/6=2+3/2*3)要过程!好的追分

问题描述:

计算:3/2-5/6+7/12-9/20+…-197/9702+199/9900(提示:3/2=1+2/1*2,5/6=2+3/2*3)
要过程!
好的追分

原式=1+1/2-(1/2+1/3)+(1/3+1/4)-(1/4+1/5)……-(1/98+1/99)+(1/99+1/100)
=1+(1/2-1/2)+(-1/3+1/3)+(1/4-1/4)+(-1/5+1/5)……+(1/98-1/98)+(-1/99+1/99)+1/100
=1+1/100
=101/100

3/2=(1+2)/(1*2)= 1/(1*2) + 2/(1*2)=1/2+1
5/6=2+3/2*3 = 1/2+1/3
...
199/9900=1/99+1/100
3/2-5/6+7/12-9/20+…-197/9702+199/9900
=(1+1/2)-(1/2+1/3)+(1/3+1/4)+... + (1/99+1/100)
=1+1/100
=101/100

很简单
原式=1+1/2-(1/2+1/3)+(1/3+1/4)-(1/4+1/5)……-(1/98+1/99)+(1/99+1/100)
=1+1/2-1/2-1/3+1/3+1/4-1/4-1/5……-1/98-1/99+1/99+1/100
=1+1/100
=101/100

原式=(1+1/2)-(1/2+1/3)+(1/3+1/4)-(1/4+1/5)+...-(1/98+1/99)+(1/99+1/100)
=1+1/2-1/2-1/3+1/3+1/4-1/4-1/5+...-1/98-1/99+(1/99+1/100)
=1+1/100
=101/100