- #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

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- Thread starter student34
- Start date

- #1

- 346

- 3

2n

Ʃ (k)

k=1

2n

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

k=1

- #2

Dick

Science Advisor

Homework Helper

- 26,260

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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

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

Science Advisor

Homework Helper

Dearly Missed

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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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