数列 极限的题目,

题目

数列 极限的题目,
lim
m→+∞
[(m-1)/1+(m-2)/2+(m-3)/3+.+3/(m-3)+2/(m-2)+1/(m-1)]/m
请问等于多少,
先不看极限,+到1/(m-1),比如m是10,就是9/1+8/2+7/3+6/4+5/5+4/6+3/7+2/8+1/9

答案

[(m-1)/1+(m-2)/2+(m-3)/3+.+3/(m-3)+2/(m-2)+1/(m-1)]/m
=[m(1+1/2+1/3+……+1/m)-m]/m
=(1+1/2+1/3+……+1/m)-1
=lnm－1＋欧拉（EULER）常数γ,
近似计算γ=0.5772156.