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  • 32n -1 is divisible by 8, for all natural numbers n.

3^{2n -1} is divisible by 8, for all natural numbers n.

 

Answers (1)

p(n)= 3^{2n -1} is divisible by 8.......(given)

Now, we’ll substitute different values for n,

p(0) = 3^0 -1 = 0, is divisible by 8

P(1) = 3^2 -1 = 8, is divisible by 8

P(2) = 3^4 -1 = 80 , is divisible by 8

Now, let us consider,

P(k) = 3^{2k} -1 be divisible by 8

Thus, P(k+1) = 3^{2(k+1)} -1 = 72x + 8, is divisible by 8

Hence, by mathematical induction,

For each natural no. n it is true that, P(n) = 3^{2n} -1 is divisible by 8.

Posted by

infoexpert21

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