A positive number is such that its fract...

A positive number is such that its fractional part, its integral part and the number itself constitute the first three terms of a geometrical progression. Show that the `n^(th)` term and the sum of the first n terms of the G.P. are, `2^n-2. cos^(n-2) (pi/5) and 2^n. cos^n (pi/5) -1` respectively.

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