作业帮(1/8+1/24+1/48+1/80+1/120+1/168+1/224+1/288)*128
来源：学生作业帮助网 编辑：作业帮 时间：2024/11/24 11:27:38
(1/8+1/24+1/48+1/80+1/120+1/168+1/224+1/288)*128
(1/8+1/24+1/48+1/80+1/120+1/168+1/224+1/288)*128
(1/8+1/24+1/48+1/80+1/120+1/168+1/224+1/288)*128
（1/8+1/24+1/48+1/80+1/120+1/168+1/224+1/288)×128
=128×(1/8)[1+1/3+1/6+1/10+1/15+1/21+1/28+1/36]
=128×(1/8)[1+2(1/(2×3)+1/(3×4)+1/(4×5)+1/(5×6)+1/(6×7)+1/(7×8)+1/(8×9)]
=128×(1/8)[1+2(1/2-1/3+1/3-1/4+...+1/8-1/9]
=128×(1/8)[1+2(1/2-1/9)]
=128×(1/8)[1+1-2/9]
=128×(1/8)(16/9)
=256/9
第一步提1/8
第二步提2
第三步
1/2-1/3=1/6
1/3-1/4=1/12
1/4-1/5=1/20
1/5-1/6=1/30
1/6-1/7=1/42
1/7-1/8=1/56
1/8-1/9=1/72
原式=1/2(1/2-1/4+1/4-1/6+1/6-1/8+1/8-1/10+1/10-1/12+1/12-1/14+1/14-1/16+1/16-1/18)*128
=1/2(1/2-1/18)128
=1/2(4/9)128
=4/9*64
=256/9
(1/8+1/24+1/48+1/80+1/120+1/168+1/224+1/288)*128=(1+1/3+1/6+1/10+1/15+1/21+1/28+1/36)*16=(1+1/3+1/6+1/5*5/6+1/7*7/12+1/36)*16=(1+1/3+1/6+1/6+1/12+1/36)*16=(1+2/3+1/9)*16=256/9