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If \( P(n): " 2^{2 n-1} \) is divisible by \( k \) for all \( n \varepsilon N^{\prime \prime} \) is true, then the value of ' \( k \) ' is
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The correct answer is:
\( 3 \)
Given that, $P(n):$ " $2^{2 n-1}$ is divisible by $\mathrm{k}$ for all $\mathrm{n} \mathrm{N}$ "
Thus
$2^{2 n}-1=4^{n}-1=(3+1)^{n}-1=3 m$
Therefore, the value of $\mathrm{k}$ is 3 .
Thus
$2^{2 n}-1=4^{n}-1=(3+1)^{n}-1=3 m$
Therefore, the value of $\mathrm{k}$ is 3 .
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