1/1*4+1/4*8+1/8*12+...+1/96*100=?

问题描述:

1/1*4+1/4*8+1/8*12+...+1/96*100=?

1/4*8=(1/4-1/8)/41/8*12=(1/8-1/12)/41/12*16=(1/12-1/16)/4.1/96*100=(1/96-1/100)/4所以原式=1/4+1/4(1/4-1/8+1/8-1/12+.-1/96+1/96-1/100)=1/4+1/4*(1/4-1/100)=31/100您验算下,没算错的话,...