Question

Geometric Series: Find the sum. >>

Answer 1

\[\frac{1 }{ \sqrt{1} + \sqrt{2} } + \frac{ 1 }{\sqrt{2} + \sqrt{3}} + \frac{1 }{\sqrt{3}+\sqrt{4}} \]

Answer 2

+ ... + \[\frac{ 1 }{ \sqrt{99}+\sqrt{100} }\]

Answer 3

\(\dfrac{1}{\sqrt1+\sqrt2}=\dfrac{\sqrt1-\sqrt2}{-1}=\sqrt2-\sqrt1\)

\(\dfrac{1}{\sqrt2+\sqrt3}=\dfrac{\sqrt2-\sqrt3}{-1}=\sqrt3-\sqrt2\)
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\(\dfrac{1}{\sqrt{99}+\sqrt{100}}=\dfrac{\sqrt{99}-\sqrt{100}}{-1}=\sqrt{100}-\sqrt{99}\)
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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?

Answer 4

i dont get it am i suppose to add only the numbers that are present/given?

Answer 5

Have you ever read it? You reply immediately " I don't get it", I would like to know where you don't get.

Answer 6

because we had this formula,

Answer 7

Sometimes, we don't have to use formula when you have a shorter way to find the sum out.

Answer 8

And the question is "Find the sum"