1^2/1^3-(1^2+2^2)/(1^3+2^3)+.-(1^2+2^2+...+80^2)/(1^3+2^3+.+
1个回答

1^2+2^2+.n^2=n(n+1)(2n+1)/6

1^3+2^3)+.n^3=n^2*(n+1)^2/4

(1^2+2^2+.n^2)/(1^3+2^3)+.n^3)

=n(n+1)(2n+1)/6/n^2*(n+1)^2/4

=2(2n+1)/3n(n+1)

=2/3{1/n+1/(n+1)}

1^2/1^3-(1^2+2^2)/(1^3+2^3)+.-(1^2+2^2+...+80^2)/(1^3+2^3+.+80^3)

=2/3{1+1/2-1/2-1/3+1/3+1/4-1/4-1/5+.+1/78+1/79-1/79-1/80}

=2/3(1-1/80)

=2/3*79/80

=79/120

24*(1/2*3+1/4*5+.+1/20*21)-(1/1^2+1/(1^2+2^2)+.+1/(1^2+2^2+.+10^2))

=24*(1/2-1/3+1/4-1/5+.+1/20-1/21)-24(