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Nerdgirl

  • one year ago

Find the sum of the following series. (shown below) A. 240 B. 255 C. 210 D. 510

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  1. Nerdgirl
    • one year ago
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    |dw:1434376110688:dw|

  2. Nerdgirl
    • one year ago
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    @aloud that's not one of my answers @phi PLEASE HELP!

  3. Nerdgirl
    • one year ago
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    no you ditz it's not one of them don't you get it?! it's not one of the answer choices!

  4. Nerdgirl
    • one year ago
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    @phi

  5. phi
    • one year ago
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    rewrite the problem \[\sum_{1}^{15}(2n+1)= 2\sum_{1}^{15}n+\sum_{1}^{15}1\]

  6. phi
    • one year ago
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    There is a formula to add up the numbers from 1 to n do you know it? and the second sum means add up 15 1's (which hopefully you know how to do)

  7. Nerdgirl
    • one year ago
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    Mmm.... what would you say if I said I knew it but I couldn't remember it? :p

  8. phi
    • one year ago
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    Gauss (famous mathematician), when a young kid in school was given the problem of adding up the numbers from 1 to 100, and he (clever fellow) saw a way to do it quickly. \[\sum_{k=1}^{n}k= \frac{ n(n+1) }{ 2 }\]

  9. phi
    • one year ago
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    your problem has n=15 so use that formula with n=15 and n+1 = 16

  10. Nerdgirl
    • one year ago
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    so it would be 15 (greek symbol) k=1 (1) = 15 (16)/2? @phi

  11. Nerdgirl
    • one year ago
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    @phi

  12. phi
    • one year ago
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    the sum of the numbers 1 to 15 is 15*16/2 = 15*8= 120 \[ \sum_{1}^{15}(2n+1)= 2\sum_{n=1}^{15}n+\sum_{n=1}^{15}1 \\ = 2(120) + \sum_{1}^{15}1 \] the sum of 15 ones is 15*1= 15 thus \[ \sum_{1}^{15}(2n+1)= 2\sum_{n=1}^{15}n+\sum_{n=1}^{15}1 \\ = 2(120) + 15 \] can you finish?

  13. Nerdgirl
    • one year ago
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    OMG ILY THANK YOU!!!!!!!!!!!

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