Prove the following by the principle of mathematical induction: `((2n)!)/(2^(2n)(n !)^2)lt=1/(sqrt(3n+1))` for all `n in Ndot`

Explanation

Let `P(n)` be the given statement.

Thus, we have.

P(n): frac{(2 n) !}{2^{2} n(n !)^{2}} leq frac{1}{sqrt{3 n+1}}

step1:

P(1): frac{2 !}{2^{2} cdot 1}=frac{1}{2} leq frac{1}{sqrt{3+1}}

Thus, `P(1)` is true.

Step2:

Let P(m) be true .

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