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nissn

  • 2 years ago

how to find the sum of this?

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  1. awesomeness123
    • 2 years ago
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    sum of wht

  2. nissn
    • 2 years ago
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    \[\sum_{k=1}^{\infty}\left( 2^{-k}+5^{-k+1} \right)\]

  3. satellite73
    • 2 years ago
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    break in to two parts and add

  4. satellite73
    • 2 years ago
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    first one is \[\sum_{k=1}^{\infty}\frac{1}{2^k}=1\]

  5. nissn
    • 2 years ago
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    how did you find that? (Haven't done this in a long time)

  6. nissn
    • 2 years ago
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    the sum is 9/4 (after wolframalpha) but I don't know how to find it

  7. sirm3d
    • 2 years ago
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    the first term is a geometric series with first term 1/2 and ratio 1/2, the second term is a geometric series with first term 1 and ratio 1/5 use the formula \[S=\frac{ a_1 }{ 1-r }\] to find the sum of an infinite geometric series

  8. nissn
    • 2 years ago
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    so then it is s =0.5/(1-0.5)=1 and 1/(1-1/5)=5/4 1+5/4 =9/4

  9. sirm3d
    • 2 years ago
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    that's right

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