n²+1＞n²-n=(n-1)*n则1/(n²+1)＜1/[(n-1)*n]=1/(n-1)-1/n原式=1/(1²+1)+1/(2²+1)+/1(3²+1)+...+1/(n²+1)＜1/(1²+1)+[1/(1×2)+1/(2×3)+...+1/(n-1)-1/n]=1/2+1/2-1/n=1-1/n＜1
