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anonymous

  • one year ago

hey guys hope your well ! so I have this evaluating proof problem ,can anyone help me plzzz. Its geometric series , question is : suppose m and k are integers with m<k find a formula for evaluating the sum.

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  1. anonymous
    • one year ago
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    \[\sum_{n=m}^{k} ar ^{n}\]

  2. anonymous
    • one year ago
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    \[S(n) = \frac{ a _{1}(1-r) }{ 1-r }\]

  3. anonymous
    • one year ago
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    i know this formula will drive the same way this formula did ^ but just dont know how to set up ?

  4. anonymous
    • one year ago
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    @IrishBoy123

  5. anonymous
    • one year ago
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    @IrishBoy123 mind helping?

  6. IrishBoy123
    • one year ago
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    for first n terms you have \[\large \Sigma_{k=0}^{n-1} \ a \ r^k = a \frac{1-r^n}{1-r}\]

  7. IrishBoy123
    • one year ago
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    so you can calculate 2 summations, each starting at zero and ending somewhere that leaves you with the interval you want to sum over a bit like S(8 to 10) = S(10) - S(7)

  8. IrishBoy123
    • one year ago
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    so methodically plug into that formula and see where you go

  9. anonymous
    • one year ago
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    ok thank you

  10. IrishBoy123
    • one year ago
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    ouch, you are using k and m in your problem so i have removed them to make it cleaner: \[\large \Sigma_{i=0}^{n-1} \ a \ r^i = a \frac{1-r^n}{1-r}\]

  11. IrishBoy123
    • one year ago
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    i mean......i have replaced the k by i

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