Question

一个不等式的放缩问题

1+1/4+1/9+1/16+......+1/N2<2-1/N
怎么放的

Answer 1

1+1/4+1/9....+1/N^2
=1+1/2*2+1/3*3+...1/N*N
＜1+1/1*2+1/2*3....+1/(N-1)N
=1+1-(1/2)+(1/2)-(1/3)....-1/N
=2-1/N
所以原式成立