Question
Prove by mathematical induction that -$\frac{(2 n) !}{2^{2 n}(n !)^{2}} \leq \frac{1}{(3 n+1)^{1 / 2}}$ for all positive Integers n.
Step 1
For $n=1$, we have \[ P(1) = \frac{(2 \cdot 1)!}{2^{2 \cdot 1}(1!)^{2}} \leq \frac{1}{(3 \cdot 1+1)^{1 / 2}} \] which simplifies to \[ \frac{2}{4} \leq \frac{1}{2} \] This is true as $\frac{1}{2} = \frac{1}{2}$. Show more…
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Mathematical Induction
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