-4/9,10/9,4/3,7/9,1/9 A.7/3 B 10/9 C -5/18 D -2-4/9,10/9,4/3,7/9,1/9 A.7/3 B 10/9 C -5/18 D -2

来源:学生作业帮助网 编辑:作业帮 时间:2021/06/20 17:58:16

-4/9,10/9,4/3,7/9,1/9 A.7/3 B 10/9 C -5/18 D -2-4/9,10/9,4/3,7/9,1/9 A.7/3 B 10/9 C -5/18 D -2
-4/9,10/9,4/3,7/9,1/9 A.7/3 B 10/9 C -5/18 D -2
-4/9,10/9,4/3,7/9,1/9
A.7/3 B 10/9 C -5/18 D -2

-4/9,10/9,4/3,7/9,1/9 A.7/3 B 10/9 C -5/18 D -2-4/9,10/9,4/3,7/9,1/9 A.7/3 B 10/9 C -5/18 D -2
因为对于正整数n,1/[n*(n+1)*(n+2)]=[1/(2n)]-[1/(n+1)]+{1/[2*(n+2)]}
原式=(1/4)-(1/3)+(1/8)
+(1/6)-(1/4)+(1/10)
+(1/8)-(1/5)+(1/12)
+(1/10)-(1/6)+(1/14)
+(1/12)-(1/7)+(1/16)
+(1/14)-(1/8)+(1/18)
+(1/16)-(1/9)+(1/20)
=-(1/3)+(1/8)+(1/5)+(1/6)+(1/7)+(1/8)+(1/18)+(1/20)-(1/9)-(1/7)-(1/5)
=-(1/3)+(1/4)+(1/6)+(1/18)+(1/20)-(1/9)
=(1/12)+(1/20)-(1/18)
=7/90
原式=1/3+4/3*5+6/3*5*7+8/3*5*7*9+(10/3*5*7*9*11+1/3*5*7*9*11)
=(1/3)+(4/3*5)+(6/3*5*7)+(8/3*5*7*9)+1/(3*5*7*9)
=(1/3)+(4/3*5)+(6/3*5*7)+((8+1)/(3*5*7*9)]
=(1/3)+(4/3*5)+[(6+1)/(3*5*7)]
=(1/3)+[(4+1)/(3*5)]
=2/3