The range of `f(x)=[1+sinx]+[2+s in2/x]+[3+s in x/3]++[n+s in x/n]AAx in [0,pi]` , where [.] denotes the greatest integer function, is, `{(n+n-2^2)/2,(n(n+1))/2}` `{(n(n+1))/2}` `{(n^2+n-2^)/2,(n(n+1))/2(n^2+n+2)/2}` `[(n(n+1))/2,(n^2+n+2)/2]`

Options

A. `{(n^(2)+n-2)/(2),(n(n+1))/(2)}`
B. `{(n(n+1))/(2)}`
C. `{(n^(2)+n-2)/(2),(n(n+1))/(2),(n^(2)+n+2)/(2)}`
D. `{(n(n+1))/(2),(n^(2)+n+2)/(2)}`

Answer

4

Explanation

`f(x)=(n(+1))/(2)+[sin x]+["sin"(x)/(2)]+...["sin"(x)/(n)]`
Range `in{((n+1))/(2),(n(n+1))/(2)+1}" as x"in[0,pi]`