Sn=1x2/2 + 2x3/2 +3x4/2+.+nx(n+1)/2 = __________

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Sn=1x2/2+2x3/2+3x4/2+.+nx(n+1)/2=__________Sn=1x2/2+2x3/2+3x4/2+.+nx(n+1)/2=__________Sn=1x2/2+2x3/2

Sn=1x2/2 + 2x3/2 +3x4/2+.+nx(n+1)/2 = __________
Sn=1x2/2 + 2x3/2 +3x4/2+.+nx(n+1)/2 = __________

Sn=1x2/2 + 2x3/2 +3x4/2+.+nx(n+1)/2 = __________
你把1/2提出来,1x2+2x3+...+n(n+1)=n(n+1)(2n+1)/6+n(n+1)/2,n(n+1)=n^2+n,然后拆开,n^2相加n(n+1)(2n+1)/6,n相加n(n+1)/2,就可以了.再把n(n+1)(2n+1)/6+n(n+1)/2除以2就可以了.

1x2/2 什么意思?

因为nx(n+1)/2=(n^2+n)/2
Sn=1x2/2 + 2x3/2 +3x4/2+......+nx(n+1)/2 = 1/2*[(1^2+2^2+3^2+...+n^2)+(1+2+3+...+n)]
=1/2*[(n(n+1)(2n+1)/6+n(n+1)/2)]
=1/2*[(n(n+1)/6](2n+1+3)
=n(n+1)(n+2)/6.
解答完毕~~·