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#1 2018-07-15 19:23:14

Zeeshan 01
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Registered: 2016-07-22
Posts: 703

Mathematical Induction

Question: For each natural number n,
               1+3+5+.......+(2n-1)=?
Why is n term is not 2n-1 ??.

Last edited by Zeeshan 01 (2018-07-15 20:23:02)


M.M.Zeeshan.K

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#2 2018-07-15 20:35:17

Alg Num Theory
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Registered: 2017-11-24
Posts: 339
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Re: Mathematical Induction

What do you mean by why is n term not 2n−1?

Since the thread title is mathematical induction, I take it you want to prove the formula for the sum of the first n odd positive integers. To do this, you need to know what the formula is in the first place. If you’re not given the formula, you can make a guess and then proceed to prove it. So, trying the first few sums …

I think you can make a guess as to what the formula is going to be.

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#3 2018-07-15 22:44:02

Zeeshan 01
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Registered: 2016-07-22
Posts: 703

Re: Mathematical Induction

nth term should be 2n-1 ?


M.M.Zeeshan.K

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#4 2018-07-16 02:24:07

bob bundy
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Registered: 2010-06-20
Posts: 8,408

Re: Mathematical Induction

Numbers of the form 2n - 1 are always odd.  You are being asked to use induction to add a set of odd numbers. When the set is just 1 + 3, there are two numbers so n = 2, but the end number is 3, not 2.  The formula 2n - 1 with n=2, has the required value 2 times 2 - 1 = 3.  In the same way when  n  = 3, the last term is 2 times 3 - 1 = 5 and so on.

Use ANT's hint to write a general formula for the sum, then prove it works by induction.

Bob


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