SOLUTION: Please help me with this mathematical induction question: Suppose we want to use mathematical induction to prove the following statement for all positive integers n: 1+3+5+..

Question 986221: Please help me with this mathematical induction question:
Suppose we want to use mathematical induction to prove the following statement for all positive integers n:
1+3+5+...+(2n-1)=n^2
In the induction step, we might prove that 1+3+5+...+(2k-1)=k^2 implies the statement:
1+3+5+...+(2k-1)+(2k+1)=?
What is the correct expression in the variable k for the right side?
Thank you for your help and time.
Answer by ikleyn(52776) (Show Source): You can put this solution on YOUR website!
.
For the proof of this formula

1+3+5+...+(2n-1)=n^2

by the method of mathematical induction see the lesson Mathematical induction and arithmetic progressions in this site.

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