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

You are not logged in.

- Topics: Active | Unanswered

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

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

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,389

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.****No great discovery was ever made without a bold guess. **

Offline

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

sure！ it's right

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

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,389

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.****No great discovery was ever made without a bold guess. **

Offline

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

Offline

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

kean wrote:

sure！ it's right

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

it does not hold for all m and n

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,389

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.****No great discovery was ever made without a bold guess. **

Offline

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

**#15**let 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)*

Offline

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

Offline