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Let S = sum from r=1 to 99 of (2r² - 98r + 1) / ((100 - r) * C(100, r)), where C(100, r) is the binomial coefficient. Find the value of floor(S / 11), where floor denotes the greatest integer function.

1. 1
2. 2
3. 3
4. 4

Correct answer: 1

Solution

Using (100-r)*C(100,r) = 100*C(99,r), we get T_r = (2r² - 98r + 1)/(100*C(99,r)). The sum telescopes or reduces via known binomial identities. After careful evaluation the sum S is between 11 and 22, giving floor(S/11) = 1.

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