Answer :

f(x) = 1 – x + x2 – x3 + …….- x99 + x100


f’(x) = -1 + 2x – 3x2 + ……. – 99x98 + 100x99


f’(1) = -1 + 2(1) – 3(1)2 + ……. – 99(1)98 + 100(1)99


= (-1 – 3 – 5…… -99) + (2 + 4 + 6 +….. + 100)
=


[Using Arithmetic Progression, where d = -2 & 2, a = -1 & 2 & n = 50 respectively]


= 25 (-2 – 98) + 25 (4 + 98)


= 25 (-100) + 25 (102)


= 25 (-100 + 102)


= 25 (2)


= 50


Hence Option (D) is the correct answer.

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