计算:1/2*4+1/4*6+1/6*8...+1/198*200

解：1/2*4+1/4*6+1/6*8...+1/198*200=1/2×[2/(2×4)+2/(4×6)+2/(6×8)+...................+2/(198×200)]=1/2×(1/2-1/4+1/4-1/6+1/6-1/8+..................+1/198-1/200)=1/2×(1/2-1/200)=1/2×99/200=99/400

【如果】1/(2*4)+1/(4*6)+1/(6*8)+……+1/(198*200)那么原式=(1/4)[1/(1*2)+1/(2*3)+1/(3*4)+……+1/(99*100)]=(1/4)[(1/1-1/2)+(1/2-1/3)+(1/3-1/4)+……+(1/99-1/100)]=(1/4)(1-1/100)=99/400