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1x2+2x3+3x4+...+10x11
=1/3x(1x2x(3-0)+2x3x(4-1)+3x4x(5-2) +...+10x11x(12-9))
=1/3x((1x2x3-0x1x2)+(2x3x4-1x2x3)+(3x4x5-2x3x4) +...+(10x11x12-9x10x11))
=1/3x(10x11x12)
=440
1x2+2x3+3x4+...+nx(n+1)
=1/3x(1x2x(3-0)+2x3x(4-1)+3x4x(5-2) +...+nx(n+1)x((n+2)-(n-1)))
=1/3x((1x2x3-0x1x2)+(2x3x4-1x2x3)+(3x4x5-2x3x4) +...+(nx(n+1)x(n+2)-(n-1)xnx(n+1)))
=1/3x(nx(n+1)x(n+2))
=1/3xnx(n+1)x(n+2)
=1/3x(1x2x(3-0)+2x3x(4-1)+3x4x(5-2) +...+10x11x(12-9))
=1/3x((1x2x3-0x1x2)+(2x3x4-1x2x3)+(3x4x5-2x3x4) +...+(10x11x12-9x10x11))
=1/3x(10x11x12)
=440
1x2+2x3+3x4+...+nx(n+1)
=1/3x(1x2x(3-0)+2x3x(4-1)+3x4x(5-2) +...+nx(n+1)x((n+2)-(n-1)))
=1/3x((1x2x3-0x1x2)+(2x3x4-1x2x3)+(3x4x5-2x3x4) +...+(nx(n+1)x(n+2)-(n-1)xnx(n+1)))
=1/3x(nx(n+1)x(n+2))
=1/3xnx(n+1)x(n+2)
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