求和:S(n)=n+2(n-1)+3(n-2)+...+n
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求和:S(n)=n+2(n-1)+3(n-2)+...+n
求和:S(n)=n+2(n-1)+3(n-2)+...+n
求和:S(n)=n+2(n-1)+3(n-2)+...+n
S(n)=n+2(n-1)+3(n-2)+...+n
=∑[k=1,n] (n+1-k)*k
=∑[k=1,n] k(n+1)-∑[k=1,n]k^2
=(n+1)∑[k=1,n] k-n(n+1)(2n+1)/6
=n(n+1)^2/2-n(n+1)(2n+1)/6
=n(n+1)(n+2)/6
S(n)=n+2(n-1)+3(n-2)+...+n
=∑[k=1,n] (n+1-k)*k
=∑[k=1,n] (nk+k-k^2)
=n^2(n+1)/2 + n(n+1)/2 -n(n+1)(2n+1)/6
=n(n+1)(n+2)/6
求和:S(n)=n+2(n-1)+3(n-2)+...+n
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