一乘三分之一加二乘四分之一加三乘五分之一省略号加九乘十一�
发布网友
发布时间：2024-10-20 21:06
共1个回答
热心网友
时间：2024-10-20 21:16
1/(1x3)+1/(2x4)+1/(3x5)+……+1/(9x11)
=[1/(1x3)+1/(3x5)+1/(5x7)+1/(7x9)+1/(9x11)]+[1/(2x4)+1/(4x6)+1/(6x8)+1/(8x10)]
=[1/(1x3)+1/(3x5)+1/(5x7)+1/(7x9)+1/(9x11)]+[1/(2x4)+1/(4x6)+1/(6x8)+1/(8x10)]
=1/2x[(1-1/3)+(1/3-1/5)+(1/5-1/7)+(1/7-1/9)+(1/9-1/11)]+1/2x[(1/2-1/4)+(1/4-1/6)+(1/6-1/8)+(1/8-1/10)]
=1/2x(1-1/11)+1/2x(1/2-1/10)
=5/11+2/10
=36/55
