Choose the correct answer out of 4 options given against each Question

If f(x) = 1 – x + x² – x³ … –x⁹⁹ + x¹⁰⁰, then f’(1) is equal to

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.