1*2+2*3+3*4+···100*101怎么做?

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1*2+2*3+3*4+···100*101怎么做?
1*2+2*3+3*4+···100*101怎么做?

1*2+2*3+3*4+···100*101怎么做?
1*2+2*3+3*4+···100*101
=1^2+1+2^2+2+3^2+3+···+100^2+100
=1^2+2^2+···+100^2+1+2+···+100
利用下面公式
1^2+2^2+3^2+……+n^2=n(n+1)(2n+1)/6
1+2+3+···+n=n(n+1)/2
在上式中,n=100,代入得,
1*2+2*3+3*4+···100*101=100*101*201/6+100*101/2=343400

帅！

1*2+2*3+3*4+.....+100*101
=1/3*1*2*3+1/3[2*3*4-1*2*3]+1/3[3*4*5-2*3*4]+....+1/3[100*101*102-99*100*101]
=1/3[1*2*3+2*3*4-1*2*3+3*4*5-2*3*4+...+100*101*102-99*100*101]
=1/3*100*101*102
=343400

通项：n^2+n
原式=(1^2+2^2+...100^2)+(1+2+3+...+100)
=100*(100+1)*(200+1)/6+100*(100+1)/2
=100*101*102/3
=343400
平方求和：N(N+1)(2N+1)/6
数列求和：N(N+1)/2

一楼的办法好

1*2+2*3+3*4+.....+100*101
=1/3*1*2*3+1/3[2*3*4-1*2*3]+1/3[3*4*5-2*3*4]+....+1/3[100*101*102-99*100*101]
=1/3[1*2*3+2*3*4-1*2*3+3*4*5-2*3*4+...+100*101*102-99*100*101]
=1/3*100*101*102
=343400``````````````````

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