## TomLikesPhysics 2 years ago I have a question regarding the sum stuff with the big sigma.

1. TomLikesPhysics

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

yep

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

or you could factorise quadratically but that would take way longer

5. TomLikesPhysics

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

6. daftkillz

obviously

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

the k can be omitted, actually.

9. TomLikesPhysics

How?

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

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

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

You're welcome :)

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