Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 8 - Sequences and Infinite Series - 8.2 Sequences - 8.2 Exercises - Page 617: 76

Answer

$\{2n+1\}_{n=1}^{\infty}=\{2n-3\}_{n=3}^{\infty}$

Work Step by Step

We are given the sequence: $\{a_n\}=\{2n+1\}_{n=1}^{\infty}$ As we have to start the index of the sequence $\{b_n\}$ by 2 units upper than the sequence $\{a_n\}$, it means we must substitute $n-2$ for $n$ in $\{a_n\}$ to get $b_n$: $b_n=2(n-2)+1$ $b_n=2n-4+1$ $b_n=2n-3$ Therefore we have: $\{2n+1\}_{n=1}^{\infty}=\{2n-3\}_{n=3}^{\infty}$
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