求证3/2小于1/1的平方+1/2^2+1/3^2+...+1/100000^2

Question

求证
3/2小于1/1的平方+1/2^2+1/3^2+...+1/100000^2

Answer 1

原式>1+1/4+1/(3*4)+...+1/(100000*100001)
=1+1/4+1/3-1/4+1/4-1/5+...-1/100001
=1+7/12-1/100001>3/2
原式