1/1*2*3+1/2*3*4+...+1/20*21*22=?
1个回答

1/1*2*3=(1/1-1/2-1/2+1/3)/2

1/2*3*4=(1/2-1/3-1/3+1/4)/2

1/3*4*5=(1/3-1/4-1/4+1/5)/2

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1/20*21*22=(1/20-1/21-1/21+1/22)/2

1/1*2*3+1/2*3*4+...+1/20*21*22

=(1/1-1/2-1/2+1/3+1/2-1/3-1/3+1/4+1/3-1/4-1/4+1/5+.+1/18-1/19-1/19+1/20+1/19-1/20-1/20+1/21+1/20-1/21-1/21+1/22)/2

=(1-1/2-1/21+1/22)/2

=115/462