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Xét f(x) = (x^101 - 1)/(x-1) = x^100 + x^99 + .... + x + 1
=> f'(x) = (101x^100 - x^101 + 1)/(x-1)^2 = 100x^99 + 99x^98 + ... + 2x + 1
=> f'(2) = A = (101 . 2^100 - 2^101 + 1)
= 2^100 (101 - 2) + 1 = 99.2^100 + 1
PS: Mình còn có thêm 1 cách nữa nè :-?
Ta có
A = 1 + 2.2 + 3.2^2 + .... + 100.2^99
2A = 2 + 2.2^2 + >>> + 99.2^99 + 100.2^100
=> A - 2A = 1 + 2 + 2^2 + ... + 2^99 - 100.2^100
=> A = 100.2^100 - (1 + 2 + 2^2 + .... + 2^99)
= 100.2^100 - 2^100 + 1 = 99.2^100 + 1
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