1x2Ê®2x3Ê®3x4Ê®ÇÉË㹫ʽÊÇʲô?

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1x2+2x3+3x4,

1*2+2*3+3*4=2+6+12=20 1x2+2x3+3x4=20


1X2+2X3+3X4+.NX(N+1)¹æÂÉ

Õâ¸öÊýÁеÄͨÏîan = n(n+1)¼´ an = n^2 + nn(n+1)(2n+1)ÆäÖÐ1^2 + 2^2 + 3^2 + ...+ n^2 = --------------6n(n+1)1+2+3+...+n...


1x2+2x3+3x4+...+n(n+1)=?

1x2+2x3+3x4+...+n(n+1)=1^2+1+2^2+2+3^2+3+...+n^2+n=1+2+...+n+(1^2+2^2+...+n^2)=(1+n)n/2+n(n+1)(2n+1)/6=n(n+1)/...


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1 + 3 + 6 + 10 = 1 + (1+2) + (1+2+3) + (1+2+3+4) = [ 1X2 + 2X3 + 3X4 + 4X5 ] / 2 = [ 1X2X3 + 2X3X(4-1) + 3X4X(5-2) +...


1x2+2x3+3x4+¡­+10x11=?

1x2+2x3+3x4+¡­+10x11 µÄÇó½â¹ý³Ì¿ÉÒÔͨ¹ýÖð²½Õ¹¿ªºÍ¹«Ê½»¯¼òÀ´Íê³É¡£Ê×ÏÈ£¬ÎÒÃÇ¿¼ÂÇÒ»°ãÐÎʽ 1x2+2x3+3x4+¡­+n(n+1)£¬¿ÉÒÔ½«ÆäÖØÐ´Îª 1x(1+1)+2x(2+1)+...


...2x3x4)ÓÉÒÔÉÏÈý¸öµÈʽÏà¼Ó ¿ÉµÃ1x2+2x3+3x4=1/3x...

1x2+2x3+3x4+.+10x11=1/3(1x2x3-0x1x2)+1/3(2x3x4-1x2x3)+1/3(3x4x5-2x3x4)+...+1/3(10x11x12-9x10x11)=1/3x10x11x12=440 (À¨ºÅÄÚÕý¸ºµÖÏû)...


²»ÓÃÊýѧ¹éÄÉ·¨,Ôõô֤Ã÷1x2+2x3+3x4+¡­+n(n+1)=n(n+1...

²»ÓÃÊýѧ¹éÄÉ·¨£¬Ôõô֤Ã÷1x2+2x3+3x4+¡­+n(n+1)=n(n+1)(n+2)/3£¿ÌâÄ¿£º²»ÓÃÊýѧ¹éÄÉ·¨£¬Ôõô֤Ã÷ 1¡¤2£«2¡¤3£«3¡¤4£«¡­¡­...


1x2ʮ2x3ʮ3x4ʮ+.+9x10

1*2+2*3+3*4+¡­¡­+n(n+1)=1^2+2^2+¡­¡­+n^2+1+2+3+¡­¡­+n=n(n+1)(2n+1)/6+n(n+1)/2=n(n+1)(n+2


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