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TomLikesPhysics

  • 2 years ago

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

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  1. TomLikesPhysics
    • 2 years ago
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    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
    • 2 years ago
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    yep

  3. Shadowys
    • 2 years ago
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    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
    • 2 years ago
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    or you could factorise quadratically but that would take way longer

  5. TomLikesPhysics
    • 2 years ago
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    Why do I add the 1s since there is no index k?

  6. daftkillz
    • 2 years ago
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    obviously

  7. Shadowys
    • 2 years ago
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    \[\sum_{k=1}^{n}1 = 1+1+1+1+1+......+1 =n\] 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
    • 2 years ago
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    the k can be omitted, actually.

  9. TomLikesPhysics
    • 2 years ago
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    How?

  10. Shadowys
    • 2 years ago
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    \[\sum_{k=1}^{n}=\sum_{1}^{n}\]

  11. Shadowys
    • 2 years ago
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    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
    • 2 years ago
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    Ok, now I think I get it. Thank you Shadowys for your help.

  13. Shadowys
    • 2 years ago
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    You're welcome :)

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