做个题lim[1/2×5 +1/5×8+1/8×11.+1/(3n-1)(3n+2) n→∞

题目

做个题lim[1/2×5 +1/5×8+1/8×11.+1/(3n-1)(3n+2) n→∞

答案

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