1+3+6+…+n(n+1)⼀2=?求详细步骤…

2025-02-26 08:51:00
推荐回答(2个)
回答1:

n(n+1)/2=[n(n+1)(n+2)-(n-1)n(n+1)]/6

1+3+6+…+ n(n+1)/2
=[(6-0)+(24-6)+(60-24)+...+n(n+1)(n+2)-(n-1)n(n+1)]/6
=n(n+1)(n+2)/6

回答2:

an=n(n+1)/2
2Sn=1^2+2^2+3^2+……+n^2 +1+2+3+……+n +n*1
=(n+1)(2n+1)/6 +(1+n)n/2 +n
Sn易求