Question

let p(k) be the statement "2 to the power 3n - 1" is divisible by 7. prove that if p(k) is true then p(k+1)is true.​

Answer 1

Answer:

Step-by-step explanation:

lets prove that the given statement is true for n=1;

2^(3*1-1)

=2^2

=4

which is not divisible;

hence the required statement cannot be proved right

Answer 2

Answer:

$2^{3k}$-1 is divisible by 7

Now for k+1,

$2^{3(k+1)}-1 = 2^{3k + 3} - 1 = 2^{3k}*2^{3} - 1 = 2^{3k}(7+1) - 1\\=> 7*2^{3k} + (2^{3k} - 1)\\=>  Multiple of 7 + Multiple of 7\\=> Divisible By 7$