用数学归纳法证明1/n+1/(n+1)+1/(n+2)+……1/n²>1(n∈N*,n>1)

题目

用数学归纳法证明1/n+1/(n+1)+1/(n+2)+……1/n²>1(n∈N*,n>1)

答案

n=2略n=k时有1/k+1/(k+1)+……+1/k²>1k≥2令a=1/k+1/(k+1)+……+1/k²>1则n=k+11/(k+1)+1/(k+2)+……+1/(k+1)²=a-1/k+1/(k²+1)+……+1/(k+1)²因为1/(k²+1)>1/(k+1)²1/(k²+2)...