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\[\sum_{1}^{99} \frac{ \sqrt{10+\sqrt{n}} }{ \sqrt{10-\sqrt{n}} }\]
but i want to simplify it, my book told me that answer is cot(pi/8). but idk how to get it !!!

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Other answers:

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
any ideas guys
lets try rationalise
too long this fraction, lol
4,9,25,36,49,64,81 are special here
According to Wolfram this sum is 327.36 approx.... Which is not cot pi/8 (somebody check in case I did it wrong)

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