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What does 2n on top of the summation expression do diferently than just n?

  • Thread starter student34
  • Start date
  • #1
346
3

Homework Statement



2n
Ʃ (k)
k=1

The Attempt at a Solution



2n
Ʃ (k) = 2n(2n+1)/2 (This is just a shot in the dark.)
k=1
 

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
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618

Homework Statement



2n
Ʃ (k)
k=1

The Attempt at a Solution



2n
Ʃ (k) = 2n(2n+1)/2 (This is just a shot in the dark.)
k=1
Sure. If you've shown the sum from 1 to n of k is n*(n+1)/2, then the sum to 2n is just 2n*(2n+1)/2. It's just substitution.
 
  • #3
346
3
Sure. If you've shown the sum from 1 to n of k is n*(n+1)/2, then the sum to 2n is just 2n*(2n+1)/2. It's just substitution.
So would this work too?

2n+1
Ʃ (k) = (2n+1)((2n+1)+1)/2
k=1
 
  • #4
Dick
Science Advisor
Homework Helper
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So would this work too?

2n+1
Ʃ (k) = (2n+1)((2n+1)+1)/2
k=1
Sure. Same thing.
 
  • #5
Ray Vickson
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Homework Statement



2n
Ʃ (k)
k=1

The Attempt at a Solution



2n
Ʃ (k) = 2n(2n+1)/2 (This is just a shot in the dark.)
k=1
[tex] \sum_{k=1}^N k = \frac{N(N+1)}{2},[/tex]
so if you put N = 2n you get the stated result. If you set N = 2n+1 you get the other result you stated.

RGV
 

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