## tanjung 2 years ago simplify !

1. tanjung

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2. jayz657

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

3. tanjung

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

4. jayz657

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. tanjung

any ideas guys

lets try rationalise

7. tanjung

too long this fraction, lol

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

9. estudier

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