Continuity and DifferentiabilityHard

Question

If f(x) = xn, then the value of f(1) - + ...... + -

Options

A.2n - 1
B.0
C.1
D.2n

Solution

f(x) = xn
∴ f′(x) = nxn-1, f″(x) = n(n - 1)xn-2
........................................................................
f″″ ......n times (x) = n!
Now f(1) -
= 1 - = (1 - 1)n = 0

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