Question

求使1^2＋3^2＋5^2.＋n^2小于6000成立的最大正奇数n

Answer 1

Sn=∑(2k-1)^2,k=1,到(n+1)/2

=∑(4k^2-4k+1)

=4*(n+1)/2*(n+3)/2*(n+2)/6-4*(n+1)/2*(n+3)/2/2+(n+1)/2

=(n+1)(n+3)(n+2)/6-(n+1)(n+3)/2+(n+1)/2

=(n+1)/6*[ (n^2+5n+6)-3(n+3)+3]

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

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

由Sn