求前n项和1.1/(2X5),1/(5X8),1/(8X11)...2.2^2/(1X3),4^2/(3X5),6^2/(5X7)...(2^2/(1X3)读做2的平方,分之3.下同)裂项相消法不是要你告诉我用什么方法!
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![求前n项和1.1/(2X5),1/(5X8),1/(8X11)...2.2^2/(1X3),4^2/(3X5),6^2/(5X7)...(2^2/(1X3)读做2的平方,分之3.下同)裂项相消法不是要你告诉我用什么方法!](/uploads/image/z/2000068-52-8.jpg?t=%E6%B1%82%E5%89%8Dn%E9%A1%B9%E5%92%8C1.1%2F%282X5%29%2C1%2F%285X8%29%2C1%2F%288X11%29...2.2%EF%BC%BE2%2F%281X3%29%2C4%EF%BC%BE2%2F%283X5%29%2C6%EF%BC%BE2%2F%285X7%29...%282%EF%BC%BE2%2F%281X3%29%E8%AF%BB%E5%81%9A2%E7%9A%84%E5%B9%B3%E6%96%B9%2C%E5%88%86%E4%B9%8B3.%E4%B8%8B%E5%90%8C%29%E8%A3%82%E9%A1%B9%E7%9B%B8%E6%B6%88%E6%B3%95%E4%B8%8D%E6%98%AF%E8%A6%81%E4%BD%A0%E5%91%8A%E8%AF%89%E6%88%91%E7%94%A8%E4%BB%80%E4%B9%88%E6%96%B9%E6%B3%95%21)
求前n项和1.1/(2X5),1/(5X8),1/(8X11)...2.2^2/(1X3),4^2/(3X5),6^2/(5X7)...(2^2/(1X3)读做2的平方,分之3.下同)裂项相消法不是要你告诉我用什么方法!
求前n项和
1.1/(2X5),1/(5X8),1/(8X11)...
2.2^2/(1X3),4^2/(3X5),6^2/(5X7)...(2^2/(1X3)读做2的平方,分之3.下同)
裂项相消法
不是要你告诉我用什么方法!
求前n项和1.1/(2X5),1/(5X8),1/(8X11)...2.2^2/(1X3),4^2/(3X5),6^2/(5X7)...(2^2/(1X3)读做2的平方,分之3.下同)裂项相消法不是要你告诉我用什么方法!
1/(2X5)+1/(5X8)+1/(8X11)+...+1/((3n-1)*(3n+2))
=1/3*(1/2-1/5+1/5-1/8+1/8-1/11+...+1/(3n-1)-1/(3n+2))
=1/3*(1/2-1/(3n+2))
=n/(6n+4)
2^2/(1X3)+4^2/(3X5)+6^2/(5X7)+...+(2n)^2/((2n-1)*(2n+1))
因为
(2n)^2/((2n-1)*(2n+1)
=((2n)^2-1+1)/((2n)^2-1)
=1+1/((2n)^2-1)
=1+1/2*(1/(2n-1)-1/(2n+1))
所以原式=
1+1/2*(1/1-1/3)+1+1/2*(1/3-1/5)+1+1/2*(1/5-1/7)+...+1+1/2*(1/(2n-1)-1/(2n+1))
=1*n+1/2*(1-1/3+1/3-1/5+1/5-1/7+...+1/(2n-1)-1/(2n+1))
=n+1/2*(1-1/(2n+1))
=(2n^2+2n)/(2n+1)
裂项相消法
1.=1/3(1/2-1/5+1/5-/1/8+1/8-1/11.....+1/(3n-1)-1/(3n-2) )=(3n-4)/(18n-12)
(1)观察上式可得:
1/(2X5)=(1/3)(1/2-1/5)
1/(5X8)=(1/3)(1/5-1/8)
1/(8X11)=(1/3)(1/5-1/8)
……
1/[(3n-1)(3n+2)]=(1/3)[1/(3n-1)-1/(3n+2)]
把以上的式子都加起来可得:
Sn=(1/3)[(1/2)-(1/5)+(1/5)-(1/8)...
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(1)观察上式可得:
1/(2X5)=(1/3)(1/2-1/5)
1/(5X8)=(1/3)(1/5-1/8)
1/(8X11)=(1/3)(1/5-1/8)
……
1/[(3n-1)(3n+2)]=(1/3)[1/(3n-1)-1/(3n+2)]
把以上的式子都加起来可得:
Sn=(1/3)[(1/2)-(1/5)+(1/5)-(1/8)+……+1/(3n-1)-1/(3n+2)]
=(1/3)[(1/2)-1/(3n+2)]
=n/(6n+4)
(2)帮不到你了,不过可能是用错位相减~~~
收起