1/9^2<1/(8*9)=1/8 - 1/9
1/10^2<1/(9*10)=1/9-1/10
……
1/64^2<1/(63*64)=1/63-1/64
1/9^2+1/10^2+……+1/64^2<(1/8 - 1/9)+(1/9-1/10)+……+(1/63-1/64)=1/8-1/64
将不等式两边同时加上1/8^2得
1/8^2+1/9^2+1/10^2+……+1/64^2<1/8
故1/8大于1/8^2+1/9^2+1/10^2+……+1/64^2 1/9^2<1/(8*9)=1/8 - 1/9
1/10^2<1/(9*10)=1/9-1/10
……
1/64^2<1/(63*64)=1/63-1/64
1/9^2+1/10^2+……+1/64^2<(1/8 - 1/9)+(1/9-1/10)+……+(1/63-1/64)=1/8-1/64
将不等式两边同时加上1/8^2得
1/8^2+1/9^2+1/10^2+……+1/64^2<1/8
故1/8大于1/8^2+1/9^2+1/10^2+……+1/64^2