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Question: Limit function sought

Question:Limit function sought

Alfred_F 315 Maple
complex-analysis
8 hours ago
0

In the attached file, (6) is stated as "false." However, it is possible to prove with pen and paper that term1 = term2. In (5), the limit function is sought but not determined.
What am I doing wrong?test1.mw
 

restart

term1 := (2*cos(2^n*x)+1)/(2*cos(x)+1)

(2*cos(2^n*x)+1)/(2*cos(x)+1)

 (1)

term2 := product(2*cos(2^k*x)-1, k = 0 .. n-1)

product(2*cos(2^k*x)-1, k = 0 .. n-1)

 (2)

term3 := term1*(2*cos(2^n*x)-1)/(2*cos(x)-1)

(2*cos(2^n*x)+1)*(2*cos(2^n*x)-1)/((2*cos(x)+1)*(2*cos(x)-1))

 (3)

simplify(term3)

(1+2*cos(2^(1+n)*x))/(1+2*cos(2*x))

 (4)

limit((1+2*cos(2^(1+n)*x))/(1+2*cos(2*x)), n = infinity)

limit((1+2*cos(2^(1+n)*x))/(1+2*cos(2*x)), n = infinity)

 (5)

is(term1 = term2)

false

 (6)

NULL


 

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