3.1.3. Intro To Real Analysis 3. List the first five terms of the following inductively defined sequences.xn+1 = 3xn+1,(a) x₁ = 1,(b) y₁ = 2,Yn+1 =2(yn +2/yn),=(d) S₁ = 3,(c) Z₁ = 1,Z₂ ==$2 :===-2, Zn+2= (Zn+1+Zn)/(Zn+1 — Zn),$2 := 5, Sn+2 := Sn + Sn+1•

The inductive sequences are :List the first five terms for the above inductive sequences

3. List the first five terms of the following inductively defined sequences. (a) x₁ = 1, (b) y₁ = 2, (c) Z₁ = 1, (d) S₁ = 3, == Xn+1=3x+1, := yn+1 = ½) (yn + 2/yn), - Z2 := 2, Zn+2 = (Zn+1 + Zn)/(Zn+1 − Zn), $25, Sn+2 = Sn + Sn+1.

3. List the first five terms of the following inductively defined sequences. (a) x₁ = 1, (b) y₁ = 2, (c) Z₁ = 1, (d) S₁ = 3, == Xn+1=3x+1, := yn+1 = ½) (yn + 2/yn), - Z2 := 2, Zn+2 = (Zn+1 + Zn)/(Zn+1 − Zn), $25, Sn+2 = Sn + Sn+1.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section: Chapter Questions

Problem 5RE

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Question

3.1.3. Intro To Real Analysis

3. List the first five terms of the following inductively defined sequences.
xn+1 = 3xn+1,
(a) x₁ = 1,
(b) y₁ = 2,
Yn+1 =
2
(yn +2/yn),
=
(d) S₁ = 3,
(c) Z₁ = 1,
Z₂ ==
$2 :=
==
-
2, Zn+2= (Zn+1+Zn)/(Zn+1 — Zn),
$2 := 5, Sn+2 := Sn + Sn+1•

Branch of mathematical analysis that studies real numbers, sequences, and series of real numbers and real functions. The concepts of real analysis underpin calculus and its application to it. It also includes limits, convergence, continuity, and measure theory.

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