a real sequence xn is defined inductively by x1 =1 and xn+1 = sqrt(xn +6) for...

a real sequence x_n is defined inductively by x₁ =1 and x_n+1 = sqrt(x_n +6) for every n belongs to N

a) prove by induction that x_n is increasing and x_n <3 for every n belongs to N

b) deduce that x_n converges and find its limit

Expert Solution

Colby Messinger answered 3 years ago

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