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The range of f(x)=[1+sinx]+[2+s in2/x]+[...

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]`

A

`{(n ^(2) +n-2)/(2), (n(n+1))/(2)}`

B

`{(n (n+1))/(2)}`

C

`{(n(n +1))/(2), (n ^(2) +n+2)/(2), (n ^(2)+ n+4)/(2)}`

D

`{(n (n+1))/(2), (n ^(2) +n-2)/(2)}`

Text Solution

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The correct Answer is:
D
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