Induction inequality check: $n!<n^n$
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Inductive Proof that $k!<k^k$, for $k\geq 2$.
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Proof by Induction for inequality, $\sum_{k=1}^nk^{-2}\lt2-(1/n)$
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Proof of an inequality by induction: $(1 + x_1)(1 + x_2)...(1 + x_n) \ge 1 + x_1 + x_2 + ... + x_n$
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Prove by induction $\sum \frac {1}{2^n} < 1$
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Proof of the inequality $(x+y)^n\leq 2^{n-1}(x^n+y^n)$
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Prove that: $2^n < n!$ Using Induction
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Proof that $n!\leq {(\frac{n+1}{2})}^{n}$
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Induction of inequality involving AP
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Proving a summation inequality with induction
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Prove $3^n > n^2$ by induction
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Induction Proof $4^k < 5^k$
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Demonstrate by induction the inequality: $\ln(1+n)\leq\sum_{i=1}^{n}\frac{1}{i}\leq1+\ln(n)$
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How to prove $4(n!)>2^{n+2}$ for $ n\geq 4$ with induction
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Proving this inequality by mathematical induction
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Show that $e^x > 1 + x + x^2/2! + \cdots + x^k/k!$ for $n \geq 0$, $x > 0$ by induction
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Using induction to prove that $\sum_{r=1}^n r\cdot r! =(n+1)! -1$
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getting tight bounds on n!