作业帮做个题lim[1/2×5 +1/5×8+1/8×11.+1/(3n-1)(3n+2) n→∞
来源：学生作业帮 编辑：作业帮 分类：数学作业 时间：2024/05/11 12:37:20
做个题lim[1/2×5 +1/5×8+1/8×11.+1/(3n-1)(3n+2) n→∞
1/2×5 +1/5×8+1/8×11.+1/(3n-1)(3n+2)=1/3*（1/2-1/5+1/5-1/8+...+1/(3n-1)-1/(3n+2)）
=1/3*(1/2-1/(3n+2))
所以lim(n→∞)[1/2×5 +1/5×8+1/8×11.+1/(3n-1)(3n+2) ]
=lim(n→∞)[1/3*(1/2-1/(3n+2))]
=1/3*(lim(n→∞)1/2-lim(n→∞)(1/(3n=2))
=1/3*(1/2-0)
=1/6
=1/3*(1/2-1/(3n+2))
所以lim(n→∞)[1/2×5 +1/5×8+1/8×11.+1/(3n-1)(3n+2) ]
=lim(n→∞)[1/3*(1/2-1/(3n+2))]
=1/3*(lim(n→∞)1/2-lim(n→∞)(1/(3n=2))
=1/3*(1/2-0)
=1/6
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