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#1 2005-10-22 09:52:52
- jd
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- Registered: 2005-10-02
- Posts: 37
Prove that 2n natural numbers is n(2n+1)
Could someone help I'm not sure how to do this.
"Show that the sum of the first 2n natural numbers is n(2n+1)"
It's a question from the heinemann c1 book.
I would ask the teacher again but it's half term and I don't know his phone number.
good day
Last edited by jd (2005-10-22 09:55:31)
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#2 2005-10-22 23:35:40
- jd
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- Registered: 2005-10-02
- Posts: 37
Re: Prove that 2n natural numbers is n(2n+1)
I'm really confused what does
◊0=0
◊1=1
mean?
I only started a level is there a easier way? I think I saw "S=n/2[2a + (n-1)d]" when the teacher did it.
thanks, JD
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#3 2005-10-23 16:09:46
- Jai Ganesh
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- Registered: 2005-06-28
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Re: Prove that 2n natural numbers is n(2n+1)
I only started a level is there a easier way? I think I saw "S=n/2[2a + (n-1)d]" when the teacher did it.
You can think of a sum of n natural numbers as an Arithmetic Progression and use this formula.
S = n/2[2a + (n-1)d]
Here, n = n, a = 1, d = 1
Therefore, S = n/2[2 + (n-1)1]
S = n(n+1)/2
It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
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#4 2005-10-24 07:23:30
- mathsyperson
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- Registered: 2005-06-22
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Re: Prove that 2n natural numbers is n(2n+1)
kylekatarn: You should only report abusive or spammy posts, things you think should be deleted because they are inappropriate. If you think ganesh's explanation isn't full enough, just say so within the topic.
ganesh: kylekatarn "would not accept that as a full demonstration".
Why did the vector cross the road?
It wanted to be normal.
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#5 2005-10-24 07:48:18
- mathsyperson
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Re: Prove that 2n natural numbers is n(2n+1)
Well, fair enough, then. Don't worry, we all make mistkaes.
Why did the vector cross the road?
It wanted to be normal.
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#6 2005-10-26 10:22:51
- jd
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- Registered: 2005-10-02
- Posts: 37
Re: Prove that 2n natural numbers is n(2n+1)
Thank you I get how to do it what I was confused about is "Prove that 2n natural numbers is n(2n+1)" I thought it meant prove 2+4+6+8+...+2n is n(2n+1).
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