Let a k = 10 C k for 0 ≤ k ≤ 10 , k ∈ N .If A k = a k - 1 0 0 a k for 0 ≤ k ≤ 10 and ∑ k = 1 9 A k ⋅ A k + 1 = a 0 0 b , then the value of a - b is equal to

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Quantrex Academy · Accepted Answer

Correct answer: C. 0

A k = 10 C k - 1 0 0 10 C k , A k + 1 = 10 C k 0 0 10 C k + 1 A k A k + 1 = 10 C k - 1 · 10 C k 0 0 10 C k · 10 C k + 1 ∑ k = 1 9 A k A k + 1 = C 0 10 C 1 10 + C 1 10 C 2 10 − − + C 8 10 . C 9 10 0 0 C 1 10 C 2 10 + C 2 10 C 3 10 + − − C 9 10 C 10 10 = 20 C 11 - 10 0 0 20 C 11 - 10 = a 0 0 b a = 20 C 11 - 10 b = 20 C 11 - 10

Let a k = 10 C k for 0 ≤ k ≤ 10 , k ∈ N .If A k = a k - 1 0 0 a k for 0 ≤ k ≤ 10 and ∑ k = 1 9 A k ⋅ A k + 1 = a 0 0 b , then the value of a - b is equal to

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