计算:1/2*4+1/4*6+1/6*8...+1/198*200

更新时间2022-05-08 00:35:27

1/(2*4) + 1/(4*6) + 1/(6*8) + ... + 1/(198*200)

= (1/4)[ 1/(1*2) + 1/(2*3) + 1/(3*4) + ... + 1/(99*100) ]

= (1/4)[ 1/2 + ( 1/2 - 1/3 ) + ( 1/3 - 1/4) + ... + ( 1/99 - 1/100) ]

= (1/4)[ 1/2 + 1/2 - 1/100) ]

= 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

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