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2. A sequence qn is defined by q1 = 1 and qn+1 = 2qn+2" for all n ≥ 1. Suppose you want to prove the formula qn = n.2n-1 by induction on n. In your induction step, what algebraic identity will you have to prove? (You don't actually need to prove anything or check any identities to answer this problem; just give the algebraic identity that the proof woul need.)

2. A sequence qn is defined by q1 = 1 and qn+1 = 2qn+2" for all n ≥ 1. Suppose you want to prove the formula qn = n.2n-1 by induction on n. In your induction step, what algebraic identity will you have to prove? (You don't actually need to prove anything or check any identities to answer this problem; just give the algebraic identity that the proof woul need.)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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2. A sequence \( q_n \) is defined by \( q_1 = 1 \) and \( q_{n+1} = 2q_n + 2^n \) for all \( n \geq 1 \). Suppose you want to prove the formula \( q_n = n \cdot 2^{n-1} \) by induction on \( n \). In your induction step, what algebraic identity will you have to prove? *(You don’t actually need to prove anything or check any identities to answer this problem; just give the algebraic identity that the proof would need.)*
Transcribed Image Text:2. A sequence \( q_n \) is defined by \( q_1 = 1 \) and \( q_{n+1} = 2q_n + 2^n \) for all \( n \geq 1 \). Suppose you want to prove the formula \( q_n = n \cdot 2^{n-1} \) by induction on \( n \). In your induction step, what algebraic identity will you have to prove? *(You don’t actually need to prove anything or check any identities to answer this problem; just give the algebraic identity that the proof would need.)*
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