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anonymous

  • one year ago

Geometric Series: Find the sum. >>

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  1. anonymous
    • one year ago
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    \[\frac{1 }{ \sqrt{1} + \sqrt{2} } + \frac{ 1 }{\sqrt{2} + \sqrt{3}} + \frac{1 }{\sqrt{3}+\sqrt{4}} \]

  2. anonymous
    • one year ago
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    + ... + \[\frac{ 1 }{ \sqrt{99}+\sqrt{100} }\]

  3. Loser66
    • one year ago
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    \(\dfrac{1}{\sqrt1+\sqrt2}=\dfrac{\sqrt1-\sqrt2}{-1}=\sqrt2-\sqrt1\) \(\dfrac{1}{\sqrt2+\sqrt3}=\dfrac{\sqrt2-\sqrt3}{-1}=\sqrt3-\sqrt2\) ............................................................................................................ \(\dfrac{1}{\sqrt{99}+\sqrt{100}}=\dfrac{\sqrt{99}-\sqrt{100}}{-1}=\sqrt{100}-\sqrt{99}\) ---------------------------------------------------------------------------- add them together \(\sqrt2-\sqrt 1+(\sqrt3-\sqrt2)+(\sqrt4-\sqrt3)+..........+(\sqrt100-\sqrt{99})\) open parentheses and cancel the like terms, you have \(\sqrt{100}-\sqrt1=9\) right?

  4. anonymous
    • one year ago
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    i dont get it am i suppose to add only the numbers that are present/given?

  5. Loser66
    • one year ago
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    Have you ever read it? You reply immediately " I don't get it", I would like to know where you don't get.

  6. anonymous
    • one year ago
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    because we had this formula,

  7. Loser66
    • one year ago
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    Sometimes, we don't have to use formula when you have a shorter way to find the sum out.

  8. Loser66
    • one year ago
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    And the question is "Find the sum"

  9. anonymous
    • one year ago
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    |dw:1437486768560:dw|

  10. Loser66
    • one year ago
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    It didn't say: "Use the formula to find the sum", right?

  11. anonymous
    • one year ago
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    yeha so any process will do

  12. anonymous
    • one year ago
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    the shorter way is to find the ratio right but i cant seem to find it

  13. Loser66
    • one year ago
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    It can be found, but it is too complicated.

  14. anonymous
    • one year ago
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    ohh but thats the only short way i get :((( is the thing u did also a short way ?

  15. Loser66
    • one year ago
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    ok, show me your work, please. I can check

  16. anonymous
    • one year ago
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    i tried solving it but tbh i gave up :((( we havent discussed this part tbh we only started with the series :((

  17. anonymous
    • one year ago
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    *just got started

  18. anonymous
    • one year ago
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    in ur equation, nine would be??

  19. Loser66
    • one year ago
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    sum of that series

  20. anonymous
    • one year ago
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    ohh all in all ok thank you so much i get it nowwww found a new short way thank u thank u :))))

  21. anonymous
    • one year ago
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    is ur method only applicable to equations with radical

  22. Loser66
    • one year ago
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    I don't know, depend on the question, we can apply or not.

  23. anonymous
    • one year ago
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    last q what happened to square root of four if u crossed out the like terms?

  24. anonymous
    • one year ago
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    in ur equation

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