If f(x) = x 100 + x 99 + …..+ x + 1, then f’(1) is equal to

Question

Philoid · Accepted Answer

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

We know that,

∴

⇒

⇒ f’(1) = 1 + 2 + 3 + … + 99 + 100 (total 100 terms)

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

∴ f’(1) =

Clearly, the above solution suggests that only 1 result is possible which is 5050.

Hence,

The only option (a) is the correct answer.