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Evaluate the number represented by the infinite series sqrt(1/3 + sqrt(1/3 + sqrt(1/3 + ...)))

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If a^2 - b^2 = 8 and a*b = 2, find a^16 + b^16 A piece of straight, level rail whose length is one mile in winter increases in length by one foot in summer. If the ends were firmly anchored in winter, we are to assume that the rail will become an arc of a circle in summer. How far will the center point move relative to its winter position?