Question

苦求初中 裂项求和法一共两道题：1.1（1/10）+3（1/40）+5（1/88）+7（1/154）+9（1/238）+

Answer 1

1.

(3+5+7+9+11)+1/10+1/(4*10)+1/(8*11)+1/(14*11)+1/(2*17*7)+1/(17*20)

=35+1/8+1/56+1/140

=35+1/8+1/(7*8)+1/(4*5*7)

=35 3/20

2.

1/(181*11)+1/(83*3*8)+1/1993+1/(2*997)+1/(7*15*19)+1/(4*499)+1/1997+1/(2*3*9*37)+1/1999+ 1/(4^2 *5^3)