1. Tardigrade
  2. Question
  3. Mathematics
  4. Consider a set, S=[1,2,3, ldots . n] n ∈ N. A non empty subset of S is called ' k ' if the arithmetic means of its elements is a natural number. Let αn be the number of ' k ' subsets and β n be the number of all singleton subsets αn will be

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Q. Consider a set, $S=[1,2,3, \ldots . n] n \in N$. A non empty subset of $S$ is called ' $k$ ' if the arithmetic means of its elements is a natural number. Let $\alpha_n$ be the number of ' $k$ ' subsets and $\beta_{ n }$ be the number of all singleton subsets
$\alpha_n$ will be

Sequences and Series

Solution:

Correct answer is (a) even if $\beta_n$ is even