Question

1*2+2*3+3*4+…+48*49+49*50

Answer 1

*表示乘号

设S=1*2+2*3+3*4+……n*(n+1)

则3S=1*2*3+2*3*3+3*4*3+4*5*3+……n*(n+1)*3

=1*2(3-0)+2*3(4-1)+3*4(5-2)+……n(n+1)[n+2-(n-1)]

=1*2*3+2*3*4-1*2*3+3*4*5-2*3*4+……+n(n+1)(n+2)-(n-1)n(n+1)

=n(n+1)(n+2),

所以S=n(n+1)(n+2)/3

故原式=49*(49+1)*(49+2)/3=41650

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