Mathematics · 2022
JEE Main · 25 June 2022, Shift 1 · Q4
Let f: N → 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 α for which Σ_k =1^10 f(α+ k…
Let $\displaystyle f: \mathbf{N} \rightarrow \mathbf{R}$ be a function such that $\displaystyle f(x+y)=2 f(x) f(y)$ for natural numbers $\displaystyle x$ and $\displaystyle y$. If $\displaystyle f(1)=2$, then the value of $\displaystyle \alpha$ for which
$$\sum_{\mathrm{k}=1}^{10} f(\alpha+\mathrm{k})=\frac{512}{3}\left(2^{20}-1\right)
$$
holds, is :
Official answer
(3)
$\displaystyle 4$
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JEE Main 2022 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.