Summation of $arccosleft(frac{n^2+r^2+r}{sqrt{(n^2+r^2+r)^2+n^2}}right)$
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I found this question in a book, and cannot solve it. I have to find the the sum $$S_n=sum_{r=0}^{n-1} arccosleft(frac{n^2+r^2+r}{sqrt{(n^2+r^2+r)^2+n^2}}right)$$ I tried converting this to $arctan(frac{n}{n^2+r^2+r})$ which seemed the most possible way of solving this but can't convert this into a difference of two terms which would help in telescoping the sum. So my question is: Am I on the right track or do I need to change my approach completely? Any help would be highly appreciated.
summation trigonometric-series
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edited Dec 17 '18 at 17:46
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