1*2+2*3+3*4+4*5+5*6+6*7+…+n(n+1)=n(n+1)(n+2)/3
问题描述:
1*2+2*3+3*4+4*5+5*6+6*7+…+n(n+1)=n(n+1)(n+2)/3
答
左边=2(2C2+3C2+……+(n+1)C2)
=2(3C3+3C2+4C2……+(n+1)C2)
=2(4C3+4C2……+(n+1)C2)
=2((n+1)C3+(n+1)C2)
=2 (n+2)C3
=n(n+1)(n+2)/3=右边