Mathematical Induction problem

I am having trouble understanding this problem with mathematical induction. I understand what needs to be done but i don't understand the results of this problem:
1...+3...+5...+..(2n1)=n^2
I assume the basic step that when n=1 this equation will be true on both sides.
2n1=n^2=2(1)1=1(1)^2=1 Hence the equation is true when n=1
Inductive step wants to prove if it is true for other numbers when n=k and k=k+1
2k1=k^2
2(k+1)1=(k+1)^2
2k+21=(k+1)(k+1)
2k+1=k^2+k+k+1
2k+1=k^2+2k+1The induction failed
But the tutorial claims that 1...+3....+5...+(2k+1)1=(k+1)^2 is true and their demonstration does not make sense. How is this so? What am I missing?
See Problem 2 at:https://www.tutorialspoint.com/discrete_mathematics/discrete_mathematical_induction.htm as reference to what im talking about.

The way the induction works is you begin by proving that the claim is true for n=1. then you assume it is tru for n=k and you use the assumption to prove that your claim is true for n= k+1. It seems from reading the convo that this is not very clearly understood. Try approaching the problem from this perspective.

You are the problem here, not the math

@cuntfuck but you can not be the solution always

@bunyonb said in Mathematical Induction problem:
Inductive step wants to prove if it is true for other numbers when n=k and k=k+1

@EmanresuRetne I have read that as well. It still doesn't show me how the equation i posted is right. I am under the assumption that both the LHS and RHS of the equation must be equal to 1. right? But that is not what i got.


@cuntfuck I agree lol