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Let $f$ be a function such that $f(x)\, = \,\sum\limits_{n\, - \,1}^n {\left[ {r\, + \,\cos \frac{x}{r}} \right]} $ where [.] denotes greatest integer function and $x \in [0,\pi]$, then range of   $f(x)$ is-

• A
  $\left[ {0\,,\,\frac{{n(n\, + \,1)}}{2}} \right]$
• ✓
  $\left\{ {\frac{{{n^2}\, + \,n\, - \,2}}{2}\,,\,\frac{{{n^2}\, + \,3n}}{2}\,,\,\frac{{{n^{2\,}} + \,n}}{2}} \right\}$
• C
  $\left\{ {\frac{{{n^2}\, - \,n\,}}{2}\,,\,\frac{{{n^2}\, + \,3n}}{2}} \right\}$
• D
  $\left[ {\frac{{{n^2}\, - \,n\,}}{2}\,,\,\frac{{{n^2}\, + \,3n}}{2}} \right]$