Let f be a real-valued function with domain R defined by f(x) = x2. Define a sequence (s1, s2, s3, ...) by s1 = b and sj = f(sj-1), for j = 1,2,3,4... a) assume that b=1, and find a formula for sn. b) assume that b=3, and find a formula for sn. c) prove the conjecture in part (b).

Let f be a real-valued function with domain R defined by f(x) = x2. Define a sequence (s1, s2, s3, ...) by s1 = b and sj = f(sj-1), for j = 1,2,3,4... a) assume that b=1, and find a formula for sn. b) assume that b=3, and find a formula for sn. c) prove the conjecture in part (b).

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.1: Infinite Sequences And Summation Notation

Problem 74E

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Question

Let f be a real-valued function with domain R defined by f(x) = x².

Define a sequence (s₁, s₂, s₃, ...) by s₁= b and s_j= f(s_j-1), for j = 1,2,3,4...

a) assume that b=1, and find a formula for s_n.

b) assume that b=3, and find a formula for s_n.

c) prove the conjecture in part (b).

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