Question

用放缩法证明这个不等式：∑（1/k²）＜5/3

Answer 1

1/k^2=2时,原式=1+1/2(1-1/2+1/2-1/3+.+1/k-1+1/k+1)

=1+1/2(1-1/k-1)

=3/2-1/2(k+1)