Solved: In each of 21 and 22, a sequence is specified by a recurrence relation and

Chapter 11, Problem 21

(choose chapter or problem)

In each of 21 and 22 , a sequence is specified by a recurrence relation and initial conditions. In each case,

(a) use iteration to guess an explicit formula for the sequence;

(b) use strong mathematical induction to confirm the correctness of the formula you obtained in part (a).

\(a_{k}=a_{\lfloor k / 2\rfloor}+2\), for all integers \(k \geq 2\)

\(a_{1}=1\)

Text Transcription:

a_k=a_lfloor k / 2 rfloor+2

k geq 2

a_1=1