Prove the following by using the principle of mathematical induction for all `n in N`:`3^(2n+2)-8n-9`is divisible by 8.

Explanation

Given expression is.

`3^(2n+2)-8n-9`

When `n = 1`, given expression is,

`3^4-8-9 = 81-17 = 64`

So, for `n=1`, given expession is divisible by `8`.

Let for any `k in N`, given expression is divisible by `8`.

Then, `3^(2k+2)-8k-9 = 8c->(1)`, where `c` is a natural number.


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