lim(n→∞)[1/1乘4+1/4乘7+1/7乘10+......+1/(3n-2)(3n+1)]

来源：百度知道 编辑：UC知道 时间：2024/05/31 09:01:35
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1/1乘4+1/4乘7+1/7乘10+......+1/(3n-2)(3n+1)]
=3[1/1-1/4+1/4-1/7。。。。。-1/（3n+1)]
=9n/(3n+1)

lim =3

1/(3n-2)(3n+1)=(1/3)*[1/(3n-2)-1/(3n+1)]
所以
lim(n→∞)[1/1乘4+1/4乘7+1/7乘10+......+1/(3n-2)(3n+1)]
=lim(n→∞)(1/3)[1-1/(3n+1)]
=1/3

1/(3n-2)(3n+1)=(1/3)*[1/(3n-2)-1/(3n+1)]

原式=(1/3)*(1-1/4)+(1/3)*(1/4-1/7)+……+(1/3)*[1/(3n-2)-1/(3n+1)]
=(1/3)*[1-(1/4-1/4)-(1/7-1/7)-……-1/(3n