Show me the steps and proof for the determine blue and inf is here As in the above manner we can generalize the notations(VII) by the following:(a-k+1)-1+ a(a-k+1) +aConsider ATtagIX(-11)q-19-1(p-2(q-1)(q-2)(a-k+1)9-1(42)**+ a%3Di=11,2, ..k + 11 = 0, 1,2, ..k and p2 3%3DXn-kIn+1 =(1)19-1(xn-k) + awhere the initial values r-k+! = a-k+! ,l = 0,1, 2, ..k. are nonzero real numbers and with(x-k+1)9-1 + -a for l = 0, 1, 2, ..k. . Moreover , we have studied the stability and periodicityof solutions for the generalized nonlinear rational difference equations in (1) and for some specialcases .Now consider the following notationsA1 = a4-1 + aA2 = a"-1 +a A-(p-2I[49–1)(q-2)(III)Ap == a9-1+ a A9-!p-1i=1where p 3.р-2Ap =a'II4? + aA-1where p 3.((I))i=1InXn+1(3)q-1(xn)"- + awhere (ro)- # -a.Now consider the following notationsXn+1(xn) + awhere (xo) + -aIn order to do this we introduce the following notations:Let xo = aConsider the following otations:Theorem 2.1 Suppose that {xn} is the solution of the difference equation (2)notations(I), the solutions of the difference equation (2) is given by:With the abovea/A1n-1aXn =An(II)i=1where a and a are non-zero real numbers and n 2.Theorem 2.2 Suppose that {xn} is solutions of (3 ) and the initial value Xo is an arbitrary nonzeroreal number. Let xo = a .Then ,by using the notations(III) , the solutions of (3) are given by:aA1n-1aIn =Ani =1II 49-3(IV)where xo = a and n 2 Theorem 5. Suppose that {xn} is the solution of the difference equation (1) and the initial valuesx-k+l = a_k+ll = 0,1, 2, ....k.are arbitrary nonzero real numbers .Let x_k+l = a_ktI wherel = 0,1, 2, ..k.Then ,by using the notations(IX), the solutions of the difference equation (1) aregiven by:(7)a_k+l(7)n-1a_k+lq-2II (4")**(T)Ani =1where T = 1, 2, ...k +1l = 0, 1, 2, ....k and n 2.Proof. We can the mathematical induction as in theorems(2.1) and (2.2) , to prove this theorem.

Question

Show me the steps and proof for the determine blue and inf is here As in the above manner we can generalize the notations(VII) by the following:(a-k+1)-1+ a(a-k+1) +aConsider ATtagIX(-11)q-19-1(p-2(q-1)(q-2)(a-k+1)9-1(42)**+ a%3Di=11,2, ..k + 11 = 0, 1,2, ..k and p2 3%3DXn-kIn+1 =(1)19-1(xn-k) + awhere the initial values r-k+! = a-k+! ,l = 0,1, 2, ..k. are nonzero real numbers and with(x-k+1)9-1 + -a for l = 0, 1, 2, ..k. . Moreover , we have studied the stability and periodicityof solutions for the generalized nonlinear rational difference equations in (1) and for some specialcases .Now consider the following notationsA1 = a4-1 + aA2 = a&#34;-1 +a A-(p-2I[49–1)(q-2)(III)Ap == a9-1+ a A9-!p-1i=1where p> 3.р-2Ap =a'II4? + aA-1where p > 3.((I))i=1InXn+1(3)q-1(xn)&#34;- + awhere (ro)- # -a.Now consider the following notationsXn+1(xn) + awhere (xo) + -aIn order to do this we introduce the following notations:Let xo = aConsider the following otations:Theorem 2.1 Suppose that {xn} is the solution of the difference equation (2)notations(I), the solutions of the difference equation (2) is given by:With the abovea/A1n-1aXn =An(II)i=1where a and a are non-zero real numbers and n > 2.Theorem 2.2 Suppose that {xn} is solutions of (3 ) and the initial value Xo is an arbitrary nonzeroreal number. Let xo = a .Then ,by using the notations(III) , the solutions of (3) are given by:aA1n-1aIn =Ani =1II 49-3(IV)where xo = a and n > 2 Theorem 5. Suppose that {xn} is the solution of the difference equation (1) and the initial valuesx-k+l = a_k+ll = 0,1, 2, ....k.are arbitrary nonzero real numbers .Let x_k+l = a_ktI wherel = 0,1, 2, ..k.Then ,by using the notations(IX), the solutions of the difference equation (1) aregiven by:(7)a_k+l(7)n-1a_k+lq-2II (4&#34;)**(T)Ani =1where T = 1, 2, ...k +1l = 0, 1, 2, ....k and n > 2.Proof. We can the mathematical induction as in theorems(2.1) and (2.2) , to prove this theorem.

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The equation given to us is as follows:…