10a) Consider the following sequence of numbers defined recursively: a, = 3, a, = V3, az = V3 + v3. an. = V3 + an Write the decimal approximations for the first six terms of this sequence. Prove that this sequence converges and find its limit. 10b) Consider the following sequence defined recursively by a, = va and an.1 = va + an, a > 2. where vā, ya + va, Va + va + va, - Prove this sequence converges and find its limit.
10a) Consider the following sequence of numbers defined recursively: a, = 3, a, = V3, az = V3 + v3. an. = V3 + an Write the decimal approximations for the first six terms of this sequence. Prove that this sequence converges and find its limit. 10b) Consider the following sequence defined recursively by a, = va and an.1 = va + an, a > 2. where vā, ya + va, Va + va + va, - Prove this sequence converges and find its limit.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:10a) Consider the following sequence of numbers defined recursively:
a, = 3, az = vV3, az = V3 + V3...
an,1
= V3 + an
Write the decimal approximations for the first six terms of this sequence. Prove that this
sequence converges and find its limit.
10b) Consider the following sequence defined recursively by a, = va and an.1 = Va + an, where
a > 2.
va, ya + va ,
Va + Va + vā."
Prove this sequence converges and find its limit.
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