- #1

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## Homework Statement

## The Attempt at a Solution

Is there any difference between the above expression and

Is there any relation between these two?

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- Thread starter zorro
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- #1

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Is there any difference between the above expression and

Is there any relation between these two?

- #2

VietDao29

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## Homework Statement

Are you sure there are up to 2 sigma signs in that expression? By the way, you mean [tex]C_r^n[/tex] right?

If there's just one sigma, then [tex]\sum_{0 \le r < s \le n} (C_r^n + C_s^n)[/tex] is different from [tex]\sum_{r = 0}^n \sum_{s = 0}^n (C_r^n + C_s^n)[/tex].

In the first sum [tex]\sum_{0 \le r < s \le n} (C_r^n + C_s^n)[/tex],

However, in the second sum: [tex]\sum_{r = 0}^n \sum_{s = 0}^n (C_r^n + C_s^n)[/tex],

So, in general, the second sum will have

- #3

tiny-tim

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The second one is roughly double the first, since it contains eg C

hmm … what about all the terms such as C_{1} + C_{1} ?

can you find an exact equation for the difference between the second and twice the first?

can you find an exact equation for the difference between the second and twice the first?

- #4

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Are you sure there are up to 2 sigma signs in that expression?

Yeah there are 2 sigma signs. 0<=r<s<=n is in between the two sigma signs.

can you find an exact equation for the difference between the second and twice the first?

Does that equate to

- #5

tiny-tim

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ok now write ∑∑ (C

(try it first with an easy small number for n, like n = 3, if you're stuck)

- #6

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Thanks!.... I got the answer

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