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 November 11th, 2015, 02:50 AM #1 Newbie   Joined: Nov 2015 From: Poland Posts: 4 Thanks: 0 Find the generating function for the following sequence Hello I need to find generating function for sequence : 1,1,1,1,1,1,0,0,0,0 .... $\displaystyle G(x) = 1 + x + x^2 + x^3 + x^4 + x^5 + 0x^6 + 0x^7 + 0x^8 + 0x^9 ..... = 1 + x + x^2 + x^3 + x^4 + x^5$ and then $\displaystyle G(x) = \frac{1 - x^6}{1 - x}$ Why is There $\displaystyle 1 - x^6$? Can somebody help me to understand that? November 11th, 2015, 11:07 AM #2 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 In general, $\displaystyle a^n- b^n= (a- b)(a^{n-1}+ a^{n-2}b+ a^{n-3}b^2+ \cdot\cdot\cdot+ a^2b^{n-2}+ ab^{n-2}+ b^{n-1})$. That can be proved, for example, by induction on n. In particular, with a= 1, b= x, and n= 6, $\displaystyle 1- x^6= (1- x)(1+ x+ x^2+ x^3+ x^.4+ x^5)$. Thanks from topsquark and Lambert1 Last edited by Country Boy; November 11th, 2015 at 11:10 AM. Tags find, function, generating, sequence, sequences Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post rayman Algebra 3 April 16th, 2013 05:52 AM Emilijo Number Theory 5 January 8th, 2012 07:40 AM Emilijo Number Theory 7 December 23rd, 2011 03:36 PM leonsotelo Algebra 2 December 5th, 2008 08:08 PM luna Applied Math 1 March 10th, 2008 07:49 AM

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