1x2+2x3+3x4+…+10x11=?

Question

1x2=1/3(1x2x3-0x1x2)
2x3=1/3(2x3x4-1x2x3)
3x4=1/3(3x4x5-2x3x4)
1x2+2x3+3x4=1/3x3x4x5=20
(过程）
1x2+2x3+3x4+…+n(n+1)=? 《2010汕头中考》
1x2x3+2x3x4+3x4x5+....+7x8x9=?

Answer 1

1x2+2x3+3x4+…+n(n+1)
=1x(1+1)+2x(2+1)+3x(3+1)+…n(n+1)
=(1^2+2^2+3^2+…+n^2)+(1+2+3+…+n)
=n(n+1)(2n+1)/6+n(n+1)/2
=n(n+1)[(2n+1)+3]/6

1x2+2x3+3x4+…+10x11
=10x(10+1)x[(10x2+1)+3]/6
=110x4
=440本回答被提问者采纳

Answer 2

1x2+2x3+3x4+…+n(n+1)
=1x(1+1)+2x(2+1)+3x(3+1)+…n(n+1)
=(1^2+2^2+3^2+…+n^2)+(1+2+3+…+n)
=n(n+1)(2n+1)/6+n(n+1)/2
=n(n+1)[(2n+1)+3]/6

1x2+2x3+3x4+…+10x11
=10x(10+1)x[(10x2+1)+3]/6
=110x4
=440

Answer 3

（1）=2+6+12+20+30+42+56+72+90+110=440

Answer 4

108505100

Answer 5

用机算器吧