Question

数列{an}若a1=1,a2=1+2,a3=1+2+3,a4=1+2+3+4…… S2012=a1+a2+a3……a20

Answer 1

an=1+2+...+n=n(n+1)/2=1/2*(n^2+n)

∴Sn=a1+a2+...+an

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

=1/2*[(1^2+2^2+...+n^2)+(1+2+...+n)]

=1/2*[n*(n+1)(2n+1)+n(n+1)/2]

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

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

∴S2012=.

麻烦自己算一下嘛,过程就是上面的啦!