Let be a function satisfying the functional equation:for all natural numbers and .If , find the value of such that: holds is...

Let f:N arrow 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}( 2^{20} - 1 ) holds, is holds, is: Sequence & Series (Mathematics)

Let

f: \mathbb{N} \rightarrow \mathbb{R}

be a function satisfying the functional equation:

f(x + y) = 2f(x)f(y)

for all natural numbers

x

and

y

.If

f(1) = 2

, find the value of

\alpha

such that:

\sum_{k = 1}^{10} f(\alpha + k) = \frac{512}{3}\left( 2^{20} - 1 \right)

holds is