Geometric Series: Find the sum. >>

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Geometric Series: Find the sum. >>

Mathematics
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\[\frac{1 }{ \sqrt{1} + \sqrt{2} } + \frac{ 1 }{\sqrt{2} + \sqrt{3}} + \frac{1 }{\sqrt{3}+\sqrt{4}} \]
+ ... + \[\frac{ 1 }{ \sqrt{99}+\sqrt{100} }\]
\(\dfrac{1}{\sqrt1+\sqrt2}=\dfrac{\sqrt1-\sqrt2}{-1}=\sqrt2-\sqrt1\) \(\dfrac{1}{\sqrt2+\sqrt3}=\dfrac{\sqrt2-\sqrt3}{-1}=\sqrt3-\sqrt2\) ............................................................................................................ \(\dfrac{1}{\sqrt{99}+\sqrt{100}}=\dfrac{\sqrt{99}-\sqrt{100}}{-1}=\sqrt{100}-\sqrt{99}\) ---------------------------------------------------------------------------- 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?

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Other answers:

i dont get it am i suppose to add only the numbers that are present/given?
Have you ever read it? You reply immediately " I don't get it", I would like to know where you don't get.
because we had this formula,
Sometimes, we don't have to use formula when you have a shorter way to find the sum out.
And the question is "Find the sum"
|dw:1437486768560:dw|
It didn't say: "Use the formula to find the sum", right?
yeha so any process will do
the shorter way is to find the ratio right but i cant seem to find it
It can be found, but it is too complicated.
ohh but thats the only short way i get :((( is the thing u did also a short way ?
ok, show me your work, please. I can check
i tried solving it but tbh i gave up :((( we havent discussed this part tbh we only started with the series :((
*just got started
in ur equation, nine would be??
sum of that series
ohh all in all ok thank you so much i get it nowwww found a new short way thank u thank u :))))
is ur method only applicable to equations with radical
I don't know, depend on the question, we can apply or not.
last q what happened to square root of four if u crossed out the like terms?
in ur equation

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