If f(x) = 1 – x + x² – x³ + ….. – x⁹⁹ + x¹⁰⁰, then f’(1) equals

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

We know that,

∴

⇒

⇒

⇒ f’(1) = –1+2–3+…–99+100

⇒ f’(1) = (2+4+6+8+….+98+100) – (1+3+5+…+97+99)

Both terms have 50 terms

We know that sum of n terms of an A.P =

∴ f’(1) =

Clearly above solution suggests that only 1 result is possible which is 50.

Hence,

Only option (d) is the correct answer.