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.