(1) 1/(2^2) - 1/(3^2) + … + 1/(n^2)
<1/1*2+1/2*3+……+1/n(n-1)
=1-1/2+1/2-1/3+……+1/(n-1)-1/n
=1-1/n
=(n-1)/n
所以 1/(2^2) - 1/(3^2) + … + 1/(n^2) < (n-1)/n
(2) 1/(2^2) - 1/(3^2) + … + 1/(n^2)
>1/2*3+1/3*4+……+1/n(n+1)
=1/2-1/3+1/3-1/4+……+1/n-1/(n+1)
=1/2-1/(n+1)
所以 1/2 - 1/(n+1) < 1/(2^2) - 1/(3^2) + … + 1/(n^2)
所以1/2 - 1/(n+1) < 1/(2^2) - 1/(3^2) + … + 1/(n^2) < (n-1)/n
望采纳