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Question: solve 6 please step by step...

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#5. Given a sequence fa pao, a , a, , define the sequence lbne bobt b2, by 田 b.-ao + a1 +a2 + + ak If a (x) is the generating function for (an) and b(x) is the generating function for tbnj, then show (1-x)a. This lets us write b)4 #6. Let(anpao, ai, a2, given by a,-0, ai-1, an+2-an+1 + an be the sequence of Fibonacci numbers; recall that the ordinary generating function for the Fibonacci numbers is a(x)Let (bn] be the sequence defined by bk-: ao + ai + + ak as in problem #5. Thus, bk is the sum of the Fibonacci numbers up to ak. The sequence {bn} begins 0,1,2,4,7,12, From #5, the generating function for {m} is a-x-x2)(1-x) Use partial fractions decomposition to find constants r,s,t such that sx +t = t (1-x-x2)(1-x) 1-x 1-x-x2 Explain how your results can be used to derive the identity b an+1 1. ENG 11:34 PM 1/22/2019

solve 6 please . step by step.

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