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Discrete Math: Proof using Mathematical Induction

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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.

Solution Summary

Proofs are offered using mathematical induction in this solution. Calculations and answers are provided.

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Solution:

To solve the problem using mathematical induction we have to prove it in two steps
1. First prove it for n =1
2. now considering that statement is true for n =n you have to show that statement is also true for = ...

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