求解一道奥数题。谢谢！

平平拿拿

1/2+1/8+1/24+1/48+1/80+1/120+1/168+1/224+1/288  求和

平平拿拿

:)

lianlian.z

需要过程是吗？

zhaosky

1/2+1/8+1/24+1/48+1/80+1/120+1/168+1/224+1/288
=1/2+ 1/(3^2-1)+1/(5^2-1)+1/(7^2-1)+1/(9^2-1)+1/(11^2-1)+1/(13^2-1)+1/(15^2-1)+1/(17^2-1)
=1/2+1/(3+1)(3-1)+1/(5+1)(5-1)+1/(7+1)(7-1)+1/(9+1)(9-1)+1/(11+1)(11-1)+1/(13+1)(13-1)+1/(15+1)(15-1)+1/(17+1)(17-1)
=1/2+ 1/2 ((1/2-1/4)+(1/4-1/6)+(1/6-1/8)+(1/8-1/10)+(1/10-1/12)+(1/12-1/14)+(1/14-1/16)+(1/16-1/18))
= 1/2 + 1/2 (1/2- 1/18) = 1/2 (1+1/2- 1/18) = 13/18

平平拿拿

zhaosky 发表于 12-3-2013 12:47
1/2+1/8+1/24+1/48+1/80+1/120+1/168+1/224+1/288
=1/2+ 1/(3^2-1)+1/(5^2-1)+1/(7^2-1)+1/(9^2-1)+1/(11^2 ...

谢谢！