Use mathematical induction to prove the following $n! < n^n$
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Inductive Proof that $k!<k^k$, for $k\geq 2$.
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Prove by induction that a^n+a^-n is an integer.
67527
Proof by Induction that $3^n ≥ 1+2^n$
42105
Fibonacci proof by induction
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proof by induction: sum of binomial coefficients $\sum_{k=0}^n (^n_k) = 2^n$
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Using induction to prove $2^{n-1}(1 + a_1a_2\ldots a_n) \geq (1+a_1)(1+a_2)\ldots(1+a_n)$ for $a_i \geq 1$
90789
Use induction to prove that that $8^{n} | (4n)!$ for all positive integers $n$
4077
Using induction prove $n^3-n$ is divisible by 3 whenever n is a positive number.
41784
Prove using mathematical induction that $n < 3 ^n$ for all positive integers n.
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Use Induction to prove that for all $n \in \mathbb{N}, (x^n + \frac{1}{x^n}) \in \mathbb{Z}$ if $x+\frac{1}{x}\in\mathbb{Z}$.
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proof using the mathematical induction
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How to prove this inequality $3^{n}\geq n^{2}$ for $n\geq 1$ with mathematical induction?
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Proof by induction: $n^{n+1} > (n + 1)^n$, $(1 + x)^n \ge 1 + nx$, other inequalities
18301
Proof by Induction involving Inequality and Factorials as denominators
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Prove by mathematical induction that $2n ≤ 2^n$, for all integer $n≥1$?
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Proof by Induction $n^2+n$ is even
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Prove by mathematical induction that $n^3 - n$ is divisible by $3$ for all natural number $n$