1 n=2時(shí)
1+1/2^2=5/4>3/2=2-1/2;
首項(xiàng)得證
2：設(shè)n=k時(shí)成立
1+1/2^2+1/3^2+……+1/k^2>2-1/k
3:n=k+1時(shí)
1+1/2^2+1/3^2+……+1/k^2+1/(k+1)^2>2-1/k +1/(k+1)^2
=2-(k^2+2k+1-k)/k(k+1)^2=2-[k(k+1)+1]/k(k+1)^2>2-k(k+1)/k(k+1)^2=2-1/(k+1)
命題得證