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 If f(x)=x100+x99+...+x+1 , then f′(1) is equal to

(a)   5050

(b)   5049

(c)   5051

(d)   5005

0 4 Views | Posted 2 months ago
Asked by Shiksha User

  • 1 Answer

  • A

    Answered by

    alok kumar singh | Contributor-Level 10

    2 months ago

    This is an objective Type Questions as classified in NCERT Exemplar

    Sol:

    Given  that  f(x)=x100+x99+…+x+1∴                    f'(x)=100x99+99x98+…+1So,                 f'(1)=100+99+98+…+1                                    =1002[2×100+(100−1)(−1)]=50[200−99]=50×101=5050.Hence,  the  correct  option  is  (a).

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