Prove the following by the principle of mathematical induction:`\ 5^(2n+2)-24 n-25` is divisible 576 for all `n in Ndot`

Explanation

Suppose `P(n): 5^{2 n-2}-24 n-25` is divisible by 576


Now let us check for `n=1`,



`P(1): 5^{2.1-2}-24.1-25`


`: 625-49`


`: 576`


`P(n)` is true for `n=1`. Where, `P(n)` is divisible by` 576`


Then, let us check for `P(n)` is true for `n=k`, and have to prove that `P(k+1)` is true.


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