## anonymous 3 years ago simplify !

1. anonymous

|dw:1351239983066:dw|

2. anonymous

$\sum_{1}^{99} \frac{ \sqrt{10+\sqrt{n}} }{ \sqrt{10-\sqrt{n}} }$

3. anonymous

but i want to simplify it, my book told me that answer is cot(pi/8). but idk how to get it !!!

4. anonymous

sorry im not exactly how to get you get that either since it was a sequence, the simplest form i can think of was that

5. anonymous

any ideas guys

6. anonymous

lets try rationalise

7. anonymous

too long this fraction, lol

8. anonymous

4,9,25,36,49,64,81 are special here

9. anonymous

According to Wolfram this sum is 327.36 approx.... Which is not cot pi/8 (somebody check in case I did it wrong)