设正整数m,n满足m<n且(1/m²+m)+{1/(m²+1)+m+1}+……+(1/n²+n)=1/23求m+n的值
问题描述:
设正整数m,n满足m<n且(1/m²+m)+{1/(m²+1)+m+1}+……+(1/n²+n)=1/23求m+n的值
答
(1/m²+m)+{1/(m²+1)+m+1}+……+(1/n²+n)
= 1/m -1/m+1 + 1/m+1 - 1/m+2 + .+ 1/n -1/n+1
= 1/m -1/n+1
1/m -1/n+1 = 1/23
所以 1/m > 1/23,即m22
由m是正整数,且m