Let b > 0, b = 1 and bn+1 = 0.5(bn + (b/bn)) A) Show that...

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Let b > 0, b₁ = 1 and bn+1 = 0.5(bn + (b/bn)) A) Show that if (bn) converges to M (not equal to zero) that the limit of (bn) as n tends to infinity is the root of b. This can be done using the arithmetic rules for sequences and the fact that bn > 0 for all n. 2 B) Given that Pn(x)=x²-2bn+1x + b show that 4bn+1² 1².4b 20 2 C) Show that bn -bn+1 = 0.5((bn+b)/bn) and then use this to confirm that bn converges Let b > 0, b₁ = 1 and bn+1 = 0.5(bn + (b/bn)) A) Show that if (bn) converges to M (not equal to zero) that the limit of (bn) as n tends to infinity is the root of b. This can be done using the arithmetic rules for sequences and the fact that bn > 0 for all n. 2 B) Given that Pn(x)=x²-2bn+1x + b show that 4bn+1² 1².4b 20 2 C) Show that bn -bn+1 = 0.5((bn+b)/bn) and then use this to confirm that bn converges