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Given these sets of equations, prove whether or not the point (xn, yn, zn) converges where n approaches infinity. If it does converge, determine the point of convergence denoted by (x, y, z) in exact form. 

 

Hint: rearrange the equations.

 

xn+1 = (2y2n+1 - z2n + 2xn + 7) / 4

yn+1 = (2z2n+1 - x2n + √(52yn) + 7) / √208

zn+1 = (-2x2n+1 + y2n + √(28zn) - 7) / 2√28

 
 Oct 4, 2022

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