Question

(2^3n-1) is divisible by ​

Answer 1

Answer:

I THINK YOUR QUESTION IS INCORRECT ❤❤❤

Answer 2

Answer:

2power 3n is divisible by 7

Step-by-step explanation:

P(n):2

3n

−1

If It's divisible by 7 then,

Base case:

n=1 then,

P(n):2

3n

−1=2

3×1

−1=7

If n=k is true for some natural numbers, then It should also be true for (k+1),

For n=k,

P(k):2

3k

−1=7d

P(k):2

3k

=7d+1 .....(1)

Where d=1,2,3,4.......so on

Now we check for n=k+1,

P(k+1):2

3(k+1)

−1=7d

P(k+1):2

3k+3

=7d+1

(Since a

xy

=a

x

a

y

)

P(k+1):2

3k

2

3

=7d+1

Substituting value from equation (1),

P(k+1):(7d+1)×8=7d+1

56d+8=7d+1

7×(8d+1)=7d

So, it is true for both k and (k+1).

Hence, from the principle of mathematical induction,

2

3n

−1 is divisible by 7 for all natural numbers.