Mathematics
Let \(f:N \rightarrow R\) be a function such that \(f(x + y) =\)
\(2f(x)f(y)\) for natural numbers \(x\) and \(y\). If \(f(1) = 2\),
then the value of \(\alpha\) for which
\(\sum_{k = 1}^{10}\mspace{2mu} f(\alpha + k) = \frac{512}{3}\left( 2^{20} - 1 \right)\)\\
holds, is holds, is
A
2
B
3
C
4
D
6
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