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  • Choose the correct answer out of 4 options given against each Question If f(x) = x100 + x99 + … x + 1, then f’(1) is equal to A. 5050 B. 5049 C. 5051 D. 50051

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

If f(x) = x\textsuperscript{100} + x\textsuperscript{99} + \ldots x + 1,, then f’(1) is equal to
A. 5050
B. 5049
C. 5051
D. 50051

Answers (1)

\\ f \left( x \right) =x^{100}+x^{99}+ \ldots +x+1 \\ \\ f^{'} \left( x \right) =100x^{99}+99x^{98}+ \ldots +1+0 \\ \\ f^{'} \left( 1 \right) =100+99+98+ \ldots +2+1=\frac{100 *101}{2}=5050 \\ \\

Hence, the answer is option A

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