Question

7^n-3^n is multiple of 4
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Answer 1

Answer:

P(K) = 7k – 3k is divisible by 4. We now have to prove P(K+1) is divi9sible by 4 whenever P(K) is true. Hence, we can see that 7K+1 – 3k+1 is divisible by 4. Thus P(K+1) is true when P(K) is true.

Step-by-step explanation:

hope it helps you bro have a great day

Answer 2

Answer: P(n):7^n-3^n is divisible by 4 is true.

Step-by-step explanation:

Consider P(n):7^n−3 ^n is divisible by 4

Now,

P(1):7^1 −3^1=4

Thus, it is true for n=1

Let p(k) is true for n=K

7^k−3^k

isdivisibleby4

Now, prov that P(k+1) is true.

7 ^(k+1) −3^(k+1)

=7^(k+1) −7.3 ^k+7.3^k −3^(k+1)

=7(7^k−3^k)+(7−3)3^k

=7(4d)+(7−3)3^k

=7(4d)+4.3^k=4(7d+3^k )

Hence, P(n):7^n-3^n is divisible by 4 is true.