- Exercise 2 Consider The Recursively Defined Sequence An N With A An A 2 1 1 201 An 1 For N E N And Initial 1 (35.78 KiB) Viewed 26 times
Exercise 2: Consider the recursively defined sequence (an)n with a² (an+/-) a ²/2 + 1/1/201 an+1 = for n E N and initial
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Exercise 2: Consider the recursively defined sequence (an)n with a² (an+/-) a ²/2 + 1/1/201 an+1 = for n E N and initial
Exercise 2: Consider the recursively defined sequence (an)n with a² (an+/-) a ²/2 + 1/1/201 an+1 = for n E N and initial value a₁ € [0, 1]. (a) Prove that an € [0, 1] for all n € N. Hint: Compute the quantity 1 - an+1. (b) Show that the sequence converges. (c) Compute the limit of the sequence depending on the value of a₁.
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