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Use mathematical induction to prove the following statements are true

  • Thread starter Daaniyaal
  • Start date
  • #1
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Homework Statement


Use mathematical induction to prove the following statements are true for n≥1

a) 1^2+3^2+5^2+...+(2n-1)^2= [n(4n-1)]/3

Homework Equations





The Attempt at a Solution


Attempt at showing for n+1 is true:

n[4(n+1-1)]/3+ 2[k+1-1)^2
 

Answers and Replies

  • #2
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First off start by letting n=1 and check it. Then you can go to n+1.
 
  • #3
HallsofIvy
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Homework Statement


Use mathematical induction to prove the following statements are true for n≥1

a) 1^2+3^2+5^2+...+(2n-1)^2= [n(4n-1)]/3

Homework Equations





The Attempt at a Solution


Attempt at showing for n+1 is true:

n[4(n+1-1)]/3+ 2[k+1-1)^2
First, what you are trying to prove true is an equation, and you have not "=". It looks to me like this is the right side of n= k with the new term added- but there are several errors.
First, bcause the term on the left is to be the "old" sum, you should not have "n+1" in place of n in 4(n-1)/3 but you should have 4(k-1)/3, not n. Second, in the sum the last term is (2n-1)^2- that is all squared so replacing n with k+ 1 gives (2(k+1)+1)^2 NOT "2[k+1-1]^2".

Since you want to prove the original statement is true for all n, it is a good idea to use "k" and "k+1" for the induction step. But do not mix "k" and "n".
 
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