Problem 1: Inductive proofs a) Prove by induction that 2 · 2 + 3 · 2² + 4 · 2³+ n≥ 3. ... ' (n + 1) 2n = n. 2n+1 for all b) Prove by induction that 3² – 1 is divisible by 8 for all n ≥ 2. -

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
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Chapter10: Sequences, Series, And Probability
Section10.4: Mathematical Induction
Problem 10E
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Problem 1: Inductive proofs
a) Prove by induction that 2 · 2 + 3 · 2² + 4 · 2³+
n≥ 3.
...
'
(n + 1) 2n = n. 2n+1 for all
b) Prove by induction that 3² – 1 is divisible by 8 for all n ≥ 2.
-
Transcribed Image Text:Problem 1: Inductive proofs a) Prove by induction that 2 · 2 + 3 · 2² + 4 · 2³+ n≥ 3. ... ' (n + 1) 2n = n. 2n+1 for all b) Prove by induction that 3² – 1 is divisible by 8 for all n ≥ 2. -
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