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

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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**Alg Num Theory****Member**- Registered: 2017-11-24
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What do you mean by why is *n* term not 2*n*−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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**Zeeshan 01****Member**- Registered: 2016-07-22
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nth term should be 2n-1 ?

M.M.Zeeshan.K

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

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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