## anonymous one year ago Geometric Series: Find the sum. >>

1. anonymous

$\frac{1 }{ \sqrt{1} + \sqrt{2} } + \frac{ 1 }{\sqrt{2} + \sqrt{3}} + \frac{1 }{\sqrt{3}+\sqrt{4}}$

2. anonymous

+ ... + $\frac{ 1 }{ \sqrt{99}+\sqrt{100} }$

3. Loser66

$$\dfrac{1}{\sqrt1+\sqrt2}=\dfrac{\sqrt1-\sqrt2}{-1}=\sqrt2-\sqrt1$$ $$\dfrac{1}{\sqrt2+\sqrt3}=\dfrac{\sqrt2-\sqrt3}{-1}=\sqrt3-\sqrt2$$ ............................................................................................................ $$\dfrac{1}{\sqrt{99}+\sqrt{100}}=\dfrac{\sqrt{99}-\sqrt{100}}{-1}=\sqrt{100}-\sqrt{99}$$ ---------------------------------------------------------------------------- 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

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

5. Loser66

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

7. Loser66

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

8. Loser66

And the question is "Find the sum"

9. anonymous

|dw:1437486768560:dw|

10. Loser66

It didn't say: "Use the formula to find the sum", right?

11. anonymous

yeha so any process will do

12. anonymous

the shorter way is to find the ratio right but i cant seem to find it

13. Loser66

It can be found, but it is too complicated.

14. anonymous

ohh but thats the only short way i get :((( is the thing u did also a short way ?

15. Loser66

16. anonymous

i tried solving it but tbh i gave up :((( we havent discussed this part tbh we only started with the series :((

17. anonymous

*just got started

18. anonymous

in ur equation, nine would be??

19. Loser66

sum of that series

20. anonymous

ohh all in all ok thank you so much i get it nowwww found a new short way thank u thank u :))))

21. anonymous

is ur method only applicable to equations with radical

22. Loser66

I don't know, depend on the question, we can apply or not.

23. anonymous

last q what happened to square root of four if u crossed out the like terms?

24. anonymous

in ur equation