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