数列求和:Sn=1/1*2*3+1/2*3*4+.+1/n*(n+1)*(n+2) 求Sn

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数列求和:Sn=1/1*2*3+1/2*3*4+.+1/n*(n+1)*(n+2) 求Sn
数列求和:Sn=1/1*2*3+1/2*3*4+.+1/n*(n+1)*(n+2) 求Sn

数列求和:Sn=1/1*2*3+1/2*3*4+.+1/n*(n+1)*(n+2) 求Sn
1/n*(n+1)*(n+2)=0.5/n-1/(n+1)+0.5/(n+2)
Sn=[1-1/2-1/(n+1)+1/(n+2)]/2=[1/2-1/(n+1)+1/(n+2)]/2

裂项法求和

1/n(n+1)(n+2)=1/2*[1/n+1/(n+2)-2/(n+1)]
Sn=1/1*2*3+1/2*3*4+......+1/n*(n+1)*(n+2)
=1/2*[1-1/2-1/(n+1)+1/(n+2)]
=n(n+3)/[4(n+1)(n+2)]