# Math Is Fun Forum

Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫  π  -¹ ² ³ °

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## #26 2009-05-18 20:40:28

Kurre
Member
Registered: 2006-07-18
Posts: 280

### Re: Kurre's Exercises

Last edited by Kurre (2009-05-18 20:41:16)

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## #27 2009-05-22 07:58:04

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Kurre's Exercises

Hi Kurre;

Will you please post your solution to #7. I have been using summation by parts, abels transformation, exponential substitution to get a geometric sum and all the trig identities I know.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #28 2009-05-22 10:39:45

kean
Member
Registered: 2009-05-17
Posts: 8

### Re: Kurre's Exercises

sure！ it's right

\sum_{k=1}^n \zeta_k^m =0

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## #29 2009-05-22 15:27:34

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Kurre's Exercises

Hi Bo Li;

Welcome to the forum.

You forgot to enclose your latex between {math}{/math} with [ replacing { and ] replacing } so it looks like this:

Anyway, how does this prove # 14

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #30 2009-05-23 00:04:13

Kurre
Member
Registered: 2006-07-18
Posts: 280

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## #31 2009-05-23 00:31:08

Kurre
Member
Registered: 2006-07-18
Posts: 280

### Re: Kurre's Exercises

kean wrote:

sure！ it's right

\sum_{k=1}^n \zeta_k^m =0

it does not hold for all m and n

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## #32 2009-05-23 00:37:58

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Kurre's Exercises

Thanks Kurre for providing the answer to #7.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #33 2009-05-24 21:40:00

Kurre
Member
Registered: 2006-07-18
Posts: 280

### Re: Kurre's Exercises

#15let k,n be positive integers, a a nonzero real, k<n+1 . Show that:

both with real analysis and by using residue calculus

edit: i did a mistake so i dont know if its possible to do this using residues, but that does not mean it must be impossible

Last edited by Kurre (2009-05-25 06:43:09)

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## #34 2009-05-27 21:12:01

Kurre
Member
Registered: 2006-07-18
Posts: 280

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