## TomLikesPhysics Group Title I have a question regarding the sum stuff with the big sigma. one year ago one year ago

1. TomLikesPhysics Group Title

According to my book this is true: $\sum_{k=1}^{n}1=n$ Why is this sum n and not 1 or 0 since there is nothing to sum?

2. daftkillz Group Title

yep

3. Shadowys Group Title

there is. The summation notation means that 1 is added n times. So, it's 1+1+1+1+1+1+1+1...+1 {n times }=n

4. daftkillz Group Title

or you could factorise quadratically but that would take way longer

5. TomLikesPhysics Group Title

Why do I add the 1s since there is no index k?

6. daftkillz Group Title

obviously

7. Shadowys Group Title

$\sum_{k=1}^{n}1 = 1+1+1+1+1+......+1 =n$ if there is no k, then there is none. k=1 simply means you start from first terms. in this case,it's 1

8. Shadowys Group Title

the k can be omitted, actually.

9. TomLikesPhysics Group Title

How?

10. Shadowys Group Title

$\sum_{k=1}^{n}=\sum_{1}^{n}$

11. Shadowys Group Title

writing k is mostly a formality but in this case without the index, then we simply ignore it and just add up 1s n times

12. TomLikesPhysics Group Title

Ok, now I think I get it. Thank you Shadowys for your help.

13. Shadowys Group Title

You're welcome :)