Let R=(2+1)2n+1,n∈N, and f=R−[R], where [ ]denote the greatest integer function, Rf is equal to

Let $F = (\sqrt{2} - 1)^{2 n + 1} .$ Note that $0 < F < 1$

Also, $R - F = 2 m$ where

$m = 2 [^{2 n + 1} C_{1} (\sqrt{2})^{2 n} +^{2 n + 1} C_{3} (\sqrt{2})^{2 n - 2} +$ $\dots +^{2 n + 1} C_{2 n + 1}]$ is an integer

$\Rightarrow [R] + f - F = 2 m \Rightarrow f - F = 2 m - [R]$ is an integer

But $- 1 < f - F < 1$ . Thus, $f - F = 0$

$∴ R f = R F = 1$

Let $R = (\sqrt{2} + 1)^{2 n + 1}, n \in N,$ and $f = R - [R],$ where [ ]
denote the greatest integer function, $R f$ is equal to