设n是正整数,求证:1/2≤1/(n+1)+1/(n+2)+······+1/2n

问题描述:

设n是正整数,求证:1/2≤1/(n+1)+1/(n+2)+······+1/2n

证明:
因为n是正整数,所以:
1/(n+1)+1/(n+2)+······+1/2n ≥1/2n+1/2n+1/2n+······+1/2n=n/2n=1/2;
1/(n+1)+1/(n+2)+······+1/2n