C Consider The Sequence Prove That Bn 0 D Consider The Sequence Of Nested Closed Intervals Bn An 1 An In 1 (26.59 KiB) Viewed 34 times
C Consider The Sequence Prove That Bn 0 D Consider The Sequence Of Nested Closed Intervals Bn An 1 An In 2 (24.47 KiB) Viewed 34 times
c) Consider the sequence Prove that bn → 0. d) Consider the sequence of nested closed intervals bn = |an+1 = an]. - In = [min{an, an+1}, max{an, an+1}]. Each are nested by b) (In+1 C In) and these are closed intervals because of a). Hence we know by Nested Interval Property, Let a Prove (an) → a 1 In 0. nIn ‡ p. n=1
Let (an) be a sequence satisfying the equation: 0; a₂ = 1 a1 1 (an+1 +2an). Show that the sequence (an) converges. We will do it in steps: an+2 = a) Show that an # an+1 for any n. b) Show that if and an+1 ≤ an an+1 ≤an+2 ≤ an an+1 anan+1 ≥ an+2 ≥ an
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