Proving Equality with Mathematical Induction | Step-by-Step Guide

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Homework Statement



Use Mathematical induction to prove that the following equality hold for any natural number n. Show your work step by step.
1+5+9+ ... +(4n-3) = n(2n-1)

Homework Equations





The Attempt at a Solution


 
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What work have you done. Do you understand how math induction works?
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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