lim[1/(1x4)+1/(4x7)+1/(7x10)+...+1/(3n-2)x(3n+1)]=_____

来源:学生作业帮助网 编辑:六六作业网 时间:2024/11/28 01:15:54
lim[1/(1x4)+1/(4x7)+1/(7x10)+...+1/(3n-2)x(3n+1)]=_____lim[1/(1x4)+1/(4x7)+1/(7x10)+...+1/(3n-2)x(3n

lim[1/(1x4)+1/(4x7)+1/(7x10)+...+1/(3n-2)x(3n+1)]=_____
lim[1/(1x4)+1/(4x7)+1/(7x10)+...+1/(3n-2)x(3n+1)]=_____

lim[1/(1x4)+1/(4x7)+1/(7x10)+...+1/(3n-2)x(3n+1)]=_____
1/(1x4)+1/(4x7)+1/(7x10)+...+1/(3n-2)x(3n+1)]
=1/3*(1-1/4+1/4-1/7+.+1/(3n-2)-1/(3n+1))
=1/3*(1-1/(3n+1))
所以
lim[1/(1x4)+1/(4x7)+1/(7x10)+...+1/(3n-2)x(3n+1)]
=lim1/3*(1-1/(3n+1))
=1/3

1/3


1/*(1*4)=1/3×[1-1/4]
1/(4*7)=1/3×[1/4-1/7]
1/(7*10)=1/3×[1/7-1/10]
.......
1/[(3n-2)*(3n+1)]=1/3×[1/(3n-2)-1/(3n+1)]
相加,得1/3×[1-1/(3n+1)]
所以,极限是1/3