The remaining problems require you to construct a mathematical proof by induction. Remember, if you don't make use of the inductive hypothesis, there is no way to finish the proof correctly! 7. Prove the following formula for all integers n ≥0: n³-7n is divisible by 3.

The remaining problems require you to construct a mathematical proof by induction. Remember, if you don't make use of the inductive hypothesis, there is no way to finish the proof correctly! 7. Prove the following formula for all integers n ≥0: n³-7n is divisible by 3.

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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Question

The remaining problems require you to construct a mathematical proof by induction. Remember, if you don’t make use of the inductive hypothesis, there is no way to finish the proof correctly!

7. Prove the following formula for all integers $ n \geq 0 $: $ n^3 - 7n $ is divisible by 3.

Expert Solution

Step 1

Follow the steps below to prove a mathematical statement using induction.

Derive the basic step and verify if $P (1)$ is true.
Derive an expression for $P (k)$ and assume the expression to be true. Here, $P (k)$ is an assumption of the induction step.
Derive the expression of $P (k + 1)$ and verify if $P (k + 1)$ satisfies the relation.

Step by step

Solved in 3 steps

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