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