Continuity and DifferentiabilityHard

Question

If y = tan-1 + tan-1 + tan-1 + ...... to n terms,then is equal to

Options

A.
B.
C.
D.None of these

Solution

y = (tan-1 (x + 1) - tan-1x) + (tan-1 (x + 2) - tan-1(x + 1)) + .....+ (tan-1 (x + n) - tan-1 (x + (n - 1)))
⇒   y = tan-1 (x + n) - tan-1 (x)
Hence, 

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