If P(n): " 2^2 n-1 is divisible by k for all n ε N^′ ′ is true, then the value of ' k ' is

Correct answer: (B) 3. Given that, P(n): " 2^2 n-1 is divisible by k for all n N " Thus 2^2 n-1=4^n-1=(3+1)^n-1=3 m Therefore, the value of k is 3 .

Q84 / 180 · KCET 2018 · Mathematics

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

A
$ 06 $
Correct answer
B
$ 3 $
C
$ 07 $
D
$ 12 $

Solution

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 .

Hence, the correct answer is option: 'B'.

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

Solution

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