Question

for every positive integer n,prove that 7n- 3n is divisible by 4

Answer 1

Answer:

for every positive integer n,  7n- 3n is divisible by 4

Step-by-step explanation:

For every positive integer n,prove that 7n- 3n is divisible by 4

Let assume than n is a positive integer

7n - 3n

= 4n

= 4 * n

=> (7n - 3n)/4  =  4n/4

=> (7n - 3n)/4 = n

While n   a positive integer  as it  was assumed

Hence (7n - 3n) is divisible by 4  as it is resulting in an integer

Hence we can say that for every positive integer n,  7n- 3n is divisible by 4

Answer 2

Answer:

Step-by-step explanation:

Let n be a positive number from the set of natural numbers.

Since n will be always on the positive side of the number line.

We have now equation f(n)= 7*n - 3*n.

Here value of n is from a natural number set and it remains constant in the function. Hence we can also simplify that function to n(7-3) = 4*n.

Now 4*n being a multiple of 2 is an even number. Hence it is also evident that 4*n is clearly divisible by 4.

We take an example as n=1 and n=2

When n=1, we have in function value of n=1, then 7n-3n comes out to be 7-3=4 which is clearly divisible by 4.

When n=2, we have value of n as 2, and the equation comes out to be 14-6 = 8 which is clearly divisible by 4.