高斯速算题1/
问题描述：
高斯速算题
1/
答
1/2(1/1-1/3+1/3-1/5....-1/99)=49/99
答
1/(1X3) = (1 - 1/3)/2
1/(3X5) = (1/3 - 1/5)/2
.....
1/(97X99) = (1/97 - 1/99)/2
所以原式=(1 - 1/3 + 1/3 - 1/5 + ... + 1/95 - 1/97 + 1/97 - 1/99)/2
= (1 - 1/99)/2
= 49/99
答
1/(1*3)+1/(3*5)+1/(5*10)+...+1/(97*99)
=1/2[(1-1/3)+(1/3-1/5)+(1/5-1/10)+...+(1/97-1/99)]
=1/2[1-1/99]
=1/2*98/99
=49/99