Explore BrainMass
Share

Discrete Math: Mathematical Induction

This content was STOLEN from BrainMass.com - View the original, and get the already-completed solution here!

Please see the attached file for the fully formatted problem.

Without using Theorem 4.2.2, use mathematical induction to prove that
P(n): 1 + 5 + 9 + ... + (4n - 3) = n(2n - 1) for all integers n >= 1

© BrainMass Inc. brainmass.com October 24, 2018, 5:17 pm ad1c9bdddf
https://brainmass.com/math/discrete-math/discrete-math-mathematical-induction-6153

Attachments

Solution Preview

Proof: n=1, P(1)=1=n(2n-1), so the statement is true for n=1.
Assume that the statement ...

Solution Summary

This solution provides proof of the statement provided through mathematical induction.

$2.19
See Also This Related BrainMass Solution

Discrete Math: Proof using Mathematical Induction

1.Use mathematical induction to prove that 2-2*7+2*7^2-.....+2(-7)^n=(1-(-7)^n+1)/4 whenever n is a nonnegative integer.

2.Show that 1^3+2^2+....n^3=[n(n+1)/2]^2 whenever n is a positive integer.

3.Use mathematical induction to show that 3 divides n^3+2n whenever n is a nonnegative integer.

View Full Posting Details