1*2+2*3+3*4+......+n*(n+1)

过称
2024-12-22 02:34:36
推荐回答(1个)
回答1:

解:
设第k项为ak
ak=k(k+1)=k²+k
1×2+2×3+...+n×(n+1)
=(1²+2²+3²+...+n²)+(1+2+3+...+n)
=n(n+1)(2n+1)/6+n(n+1)/2
=n(n+1)(n+2)/3