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Let 1+ underset(r=1)overset(10)sum(3^(r)...

Let `1+ underset(r=1)overset(10)sum(3^(r)..^(10)C_(r)+r..^(10)C_(r)) = 2^(10)(alpha. 4^(5) + beta)` where `alpha, beta in N` and `f(x) = x^(2) - k^(2) + 1`. If `alpha, beta` lies between the roots of `f(x) = `, the smalles positive integral value of k is `"____"`.

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