(1+17/96)+(1+17/96*2)+(1+17/96*3)+…+(1+17/96*94)+(1+17/96*95)1+1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/08 06:22:19
(1+17/96)+(1+17/96*2)+(1+17/96*3)+…+(1+17/96*94)+(1+17/96*95)1+1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90

(1+17/96)+(1+17/96*2)+(1+17/96*3)+…+(1+17/96*94)+(1+17/96*95)1+1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90
(1+17/96)+(1+17/96*2)+(1+17/96*3)+…+(1+17/96*94)+(1+17/96*95)
1+1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90

(1+17/96)+(1+17/96*2)+(1+17/96*3)+…+(1+17/96*94)+(1+17/96*95)1+1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90
(1+17/96)+(1+17/96*2)+(1+17/96*3)+…+(1+17/96*94)+(1+17/96*95)
=95+17/96*(1+2+3+…+95)
=95+17/96*96*95/2
=209/2
1+1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90
=1+1/(1*2)+1/(2*3)+1/(3*4)+1/(4*5)+1/(5*6)+1/(6*7)+1/(7*8)+1/(8*9)+1/(9*10)
=1+1-1/2+1/2-1/3+1/3-1/4+…+1/9-1/10
=2-1/10
=19/10

1+1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90=
1+(1-1/2)+(1/2-1/3)+(1/3-1/4)......(1/8-1/9)+(1/9-1/10)=1+1-1/10=1.9

(1+17/96)+(1+17/96*2)+(1+17/96*3)+…+(1+17/96*94)+(1+17/96*95)
=95+17/96(1+1/2+1/3+...+1/94+1/95)