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frac{1}{sqrt{3}+sqrt{7}}+frac{1}{sqrt{7}+sqrt{11}}+frac{1}{sqrt{11}+sqrt{15}}+...+frac{1}{sqrt{27}+sqrt{31}}\\-frac{sqrt{3}-sqrt{7}}{4}-frac{sqrt{7}-sqrt{11}}{4}-frac{sqrt{11}-sqrt{15}}{4}-...-frac{sqrt{27}-sqrt{31}}{4}\-frac{sqrt{3}}{4}+frac{sqrt{7}}{4}-frac{sqrt{7}}{4}+frac{sqrt{11}}{4}-frac{sqrt{11}}{4}+frac{sqrt{15}}{4}-...-frac{sqrt{27}}{4}+frac{sqrt{31}}{4}\-frac{sqrt{3}}{4}+frac{sqrt{31}}{4}=frac{sqrt{31}-sqrt{3}}{4}

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