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Exercise 0.3.11: Prove by induction that n < 2n for every natural number n. Remarks Recall from Math 300 that a proof by induction has two parts. The basis step requires checking that the statement holds for an initial value (usually easy). The induction step requires proving an implication, namely, (Vn) (n < 2″ ⇒n+1<2n+1). This step is where most of the work lies.

Exercise 0.3.11: Prove by induction that n < 2n for every natural number n. Remarks Recall from Math 300 that a proof by induction has two parts. The basis step requires checking that the statement holds for an initial value (usually easy). The induction step requires proving an implication, namely, (Vn) (n < 2″ ⇒n+1<2n+1). This step is where most of the work lies.

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter8: Sequences, Series, And Probability
Section8.5: Mathematical Induction
Problem 37E
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Exercise 0.3.11: Prove by induction that n < 2n for every natural number n. Remarks Recall from Math 300 that a proof by induction has two parts. The basis step requires checking that the statement holds for an initial value (usually easy). The induction step requires proving an implication, namely, (Vn)(n < 2″ ⇒n+1 < 2n+1). This step is where most of the work lies.
Transcribed Image Text:Exercise 0.3.11: Prove by induction that n < 2n for every natural number n. Remarks Recall from Math 300 that a proof by induction has two parts. The basis step requires checking that the statement holds for an initial value (usually easy). The induction step requires proving an implication, namely, (Vn)(n < 2″ ⇒n+1 < 2n+1). This step is where most of the work lies.
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