AI Tutor
Back to Describing Sequences

Exercise 3

Avg difficulty 2.5

Consider the sequence (an)n≥1(a_n)_{n \ge 1} that starts 1,3,5,7,9,…1, 3, 5, 7, 9, \ldots (i.e., the odd numbers in order).

  1. Give a recursive definition and closed formula for the sequence.

  2. Write out the sequence (bn)n≥2(b_n)_{n \ge 2} of partial sums of (an)(a_n). Write down the recursive definition for (bn)(b_n) and guess at the closed formula.

Levin, Discrete Mathematics: An Open Introduction (3rd ed.), §3.1 Describing Sequences, Exercise 3

AI Tutor

Adapted from Discrete Mathematics: An Open Introduction © 2013–2019 Oscar Levin. Licensed under CC BY-SA 4.0. Source: Discrete Mathematics: An Open Introduction. Imported at revision 1e2e26b.