1/3+1/15+1/35+1/63+……+1/399+1/4831/2+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:六六作业网 时间:2024/12/24 13:45:34
1/3+1/15+1/35+1/63+……+1/399+1/4831/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/901/3+1/15+1/35+1/63+……+1/3

1/3+1/15+1/35+1/63+……+1/399+1/4831/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90
1/3+1/15+1/35+1/63+……+1/399+1/483
1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90

1/3+1/15+1/35+1/63+……+1/399+1/4831/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90
1.原式=1/(1x3)+1/(3x5)+1/(5x7)+1/(7x9)+1/(9x11)+1/(11x13)+1/(11*15)+1/(15*17)+1/(17*19)+1/(21*23)
=(1-2/3)+(2/3-3/5)+(3/5-4/7)+(4/7-5/9)+(5/9-6/11)+(6/11-7/13)+(7/13-9/15)+(9/15-11/17)+(11/17-13/19)+(13/19-15/21)+(15/21-17/23)
=1-17/23
=6/23
2.
1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90
=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)
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10
=1-1/10
=9/10

1) = 1/3+ (1/3-1/5) +(1/5-1/7) + ..... +(1/21 - 1/23)
= 1/3 + 1/3 - 1/23 = 43/96
2) = 1/2+ (1/2-1/3) +(1/3-1/4) + ..... +(1/9 - 1/10)
= 1/2 + 1/2 - 1/10= 9/10