Page 1 of 1
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
Posted: Tue Jul 12, 2022 12:08 pm
by answerhappygod
- 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 43 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 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.