Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 decade ago

does this make sense to you?

just wondering why muliplying this is true.

(0.0001) ∑ k=0 to infinity [(.99)^2]^k = 0.0001 / (1-(.99)^2)

so its the .0001 multiplied by the sum from 0 to infinity multiplied by [(.99)^2]^k

why does the left side equal the right side, i dont get it

4 Answers

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  • Kim
    Lv 6
    1 decade ago
    Favorite Answer

    (0.0001) ∑ k=0 to infinity [(.99)^2]^k = 0.0001 / (1-(.99)^2)

    an infinite geometric series is S∞ = a1 / (1-r ) where r is between 0 and 1

    What you have here looks like a geometric series. See

    http://www.mathwords.com/i/infinite_geometric_seri...

    a1 = 0.0001 and r = (.99)^2

  • hippo
    Lv 6
    1 decade ago

    (0.0001) ∑ k=0 to infinity [(.99)^2]^k = 0.0001 / (1-(.99)^2)

    ∑ k=0 to infinity [(.99)^2]^k = 1 / (1-(.99)^2)

    ∑ k=0 to infinity [(.99)^(2k)] = 1 / (1-(.99)^2)

    (.99)^0 + (.99)^2 + (.99)^4 ... = 1 / (1-(.99)^2)

    (1 - (.99)^2)[(.99)^0 + (.99)^2 + (.99)^4 ...] = 1

    [(.99)^0 + (.99)^2 + (.99)^4 ...] - (.99)^2[(.99)^0 + (.99)^2 + (.99)^4 ...] = 1

    [(.99)^0 + (.99)^2 + (.99)^4 +...] - [(.99)^2 + (.99)^4 + ...] = 1

    [(.99)^0] = 1

    1 = 1

    TRUE

  • 1 decade ago

    hahahhah i have no clue srry that is hard stuff right there yup yup

  • 1 decade ago

    hmmm doesn't quite make sense to me

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