Question

The sequence {a_n} is defined by a_1 = 2, and a_{n+1} = 1/2 (a_n + 2/a_n), for n >= 1. Assuming that {a_n} converges, find its limit. lim_{n -> infinity} a_n = . Hint: Let a = lim_{n -> infinity} a_n. Then, since a_{n+1} = 1/2 (a_n + 2/a_n), we have a = 1/2 (a + 2/a). Now solve for a.

Name: The sequence an is defined by a1 = 2, and an+1 = 1/2 (an + 2/an), for n >= 1. Assuming that an converges, find its limit. limn -> infinity an = . Hint: Let a = limn -> infinity an. Then, since an+1 = 1/2 (an + 2/an), we have a = 1/2 (a + 2/a). Now solve for a.
Uploaded: 2023-01-17T05:14:33-08:00
Duration: 2 min 17 s
Channel: Madhur L
Description: The sequence an is defined by a1 = 2, and an+1 = 1/2 (an + 2/an), for n >= 1. Assuming that an converges, find its limit. limn -> infinity an = . Hint: Let a = limn -> infinity an. Then, since an+1 = 1/2 (an + 2/an), we have a = 1/2 (a + 2/a). Now solve for a.

          The sequence {a_n} is defined by a_1 = 2, and a_{n+1} = 1/2 (a_n + 2/a_n), for n >= 1. Assuming that {a_n} converges, find its limit. lim_{n -> infinity} a_n = . Hint: Let a = lim_{n -> infinity} a_n. Then, since a_{n+1} = 1/2 (a_n + 2/a_n), we have a = 1/2 (a + 2/a). Now solve for a.

The sequence an is defined by a1 = 2, and an+1 = 1/2 (an + 2/an), for n >= 1. Assuming that an converges, find its limit. limn -> infinity an = . Hint: Let a = limn -> infinity an. Then, since an+1 = 1/2 (an + 2/an), we have a = 1/2 (a + 2/a). Now solve for a.

Added by Steven B.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

01/17/2023

Step 1

Step 1: Given the sequence \(\{a_n\}\) defined by \(a_1 = 0\), \(a_2 = 1\), and \(a_{n+1} = 2(a_n)^2\) for \(n > 1\). Show more…

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The sequence {an} is defined by a1 = 0, a2 = 1, and an+1 = 2(an)^2 for n > 1. Assuming that {an} converges, find its limit. lim (an) as n approaches infinity. Hint: Let a = lim (an). Then, since a = 2(a^2), we have a = 2(a^2). Now solve for a.