求证1/(n+1)+1/(n+2)+.+1/(3n+1)>1 [n属于N*]
问题描述:
求证1/(n+1)+1/(n+2)+.+1/(3n+1)>1 [n属于N*]
答
1/(n+1)+1/(3n+1)>2/(2n+1)
1/(n+2)+1/(3n)>2/(2n+1)
.
1/(2n)+1/(2n+2)>2/(2n+1)
1/(2n+1)=1/(2n+1)
1/(n+1)+1/(n+2)+.+1/(3n+1)>(2n+1)/(2n+1)=1