Online JudgeProblem SetAuthorsOnline ContestsUser
Web Board
Home Page
F.A.Qs
Statistical Charts
Problems
Submit Problem
Online Status
Prob.ID:
Register
Update your info
Authors ranklist
 Current Contest
Past Contests
Scheduled Contests
Award Contest
User ID:
Password:
  Register

Re:prove it like this

Posted by gemenhao at 2006-04-07 14:48:19 on Problem 2539
In Reply To:prove it like this Posted by:achilles at 2005-08-08 19:51:37 
Éè a = ( k + 1 ) * ( b + 1 ) +  r
f(t,a) 	=  1 + t + t^2 + ... + t^a
		= (1 + t + t^2 + ... + t^b)( 1 + t^(b+1) + t^2(b+1) + ... + t^k(b+1) )
		  + t^(k + 1)(b + 1) + .....+ t^a

		= f(t,b) * f(t^(b+1), k) + t^(b-a) * f(t,r)

(t^a - 1) 	f(t,a)     		                  f(t, r)
__________=   _________ = f( t^(b+1),k ) + t^(k+1)(b+1) *_________
(t^b - 1) 	f(t,b)    	   		           f(t, b)

					    1 + t +... + t^r
			= f( t^(b+1),k ) +  _________________ *(t^(k+1)(b+1))
					    1 + t +... + t^b

					     t^r - 1
			= f( t^(b+1),k ) + _____________ * (t^(k+1)(b+1))
					    t^(b+1) - 1

			= f( t^(b+1),k )

			=( 1 + t^(b+1) + t^2(b+1) + ... + t^k(b+1) )
Followed by:
Post your reply here:
User ID:
Password:
Title:

Content:

Home Page   Go Back  To top

All Rights Reserved 2003-2013 Ying Fuchen,Xu Pengcheng,Xie Di
Any problem, Please Contact Administrator