Answer :
f(x)=x100 + x99 + ………….x + 1
f'(x) = 100x99 + 99x98 +…… + 1
f'(1) = 100(1)99 + 99(1)98 + …… + 1
[Using Arithmetic Progression, where d = -1, a = 100 & n = 100]
= 50 (200 – 99)
= 50 (101)
= 5050
Hence Option (A) is the correct answer.
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