Find $\frac{\sum\limits^{2499}_{k=1}{\sqrt{10+\sqrt{50+\sqrt{k}}}}}{\sum\limits^{2499}_{k=1}{\sqrt{10-\sqrt{50+\sqrt{k}}}}}$

Asked Aug 30 '13 at 08:08

Active Aug 30 '13 at 08:08

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Find the ratio,$\frac{\sum\limits^{2499}_{k=1}{\sqrt{10+\sqrt{50+\sqrt{k}}}}}{\sum\limits^{2499}_{k=1}{\sqrt{10-\sqrt{50+\sqrt{k}}}}}$

asked Aug 30 '13 at 08:08

Steven Sun

mh it is a finite problem, I guess you aren't allowed to use computer algebra systems are you ? – Dominic Michaelis Aug 30 '13 at 08:13
1

Hint: http://math.stackexchange.com/questions/464346/why-does-this-ratio-of-sums-of-square-roots-equal-1-sqrt2-sqrt42-sqrt2-co – Uwe Stroinski Aug 30 '13 at 08:20

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