Divide 2x\(^{3}\) + 11x\(^2\) + 17x + 6 by 2x + 1.

Express in partial fractions \(\frac{11x + 2}{6x^2 - x - 1}\)

If x is a positive real number, find the range of values for which \(\frac{1}{3x}\) + \(\frac{1}{2}\) > \(\frac{1}{4x}\)

The sum of the first three terms of a geometric progression is half its sum to infinity. Find the positive common ratio of the progression.