Question

两个等差数列相乘求和请问不用数学归纳法怎么做?

Answer 1

sn=1*2+2*3+...+n*(n+1)

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

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

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

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