Question

I have a question regarding the sum stuff with the big sigma.

Answer 1

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?

Answer 2

yep

Answer 3

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

Answer 4

or you could factorise quadratically but that would take way longer

Answer 5

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

Answer 6

obviously

Answer 7

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

Answer 8

the k can be omitted, actually.

Answer 9

How?

Answer 10

\[\sum_{k=1}^{n}=\sum_{1}^{n}\]

Answer 11

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

Answer 12

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

Answer 13

You're welcome :)