Question

Let a > 0 and x1 > 0. Define a sequence (xn) by xn+1 = √ a + xn. Prove that (xn) converges and find its limit.

Name: let a 0 and x1 0 define a sequence xn by xn1 a xn prove that xn converges and find its limit 98534
Uploaded: 2022-10-18T01:50:04-08:00
Duration: 3 min 29 s
Channel: Vincenzo Zaccaro
Description: let a 0 and x1 0 define a sequence xn by xn1 a xn prove that xn converges and find its limit 98534

          Let a > 0 and x1 > 0. Define a sequence (xn) by xn+1 = √ a
+ xn. Prove that (xn) converges and find its limit.

Added by Daniela R.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Vincenzo Zaccaro

10/18/2022

Step 1

We prove this by induction. For n = 1, we have x1 > 0 and x2 = √a + x1 > x1, so the statement is true for n = 1. Assume that the statement is true for some n = k, i.e., xk+1 > xk and xk+1 ≤ a + x1. We need to show that the statement is also true for n = k + Show more…

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