anonymous
  • anonymous
I have a question regarding the sum stuff with the big sigma.
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
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?
anonymous
  • anonymous
yep
anonymous
  • anonymous
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

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anonymous
  • anonymous
or you could factorise quadratically but that would take way longer
anonymous
  • anonymous
Why do I add the 1s since there is no index k?
anonymous
  • anonymous
obviously
anonymous
  • anonymous
\[\sum_{k=1}^{n}1 = 1+1+1+1+1+......+1 =n\] if there is no k, then there is none. k=1 simply means you start from first terms. in this case,it's 1
anonymous
  • anonymous
the k can be omitted, actually.
anonymous
  • anonymous
How?
anonymous
  • anonymous
\[\sum_{k=1}^{n}=\sum_{1}^{n}\]
anonymous
  • anonymous
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
anonymous
  • anonymous
Ok, now I think I get it. Thank you Shadowys for your help.
anonymous
  • anonymous
You're welcome :)

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