How can I prove through mathematical induction that $(n!)^{(1/n)}\le(n+1)/2$?
127102
Upper bound for $\sqrt[n]{n!}$
66358
Prove by mathematical induction that $2n ≤ 2^n$, for all integer $n≥1$?
150565
Prove $(a+b)^\frac{1}{n} \le a^\frac{1}{n} + b^\frac{1}{n}$
99052
Prove that $( 1 + n^{-2}) ^n \to 1$.
86479
How to Prove with Mathematical Induction $3^n > n^2$
14435
Show by induction: $(1+\frac{1}{n})^{n}<n$
40692
Proving by strong induction that $\forall n \ge 2, \;\forall d \ge 2 : d \mid n(n+1)(n+2)...(n+d-1) $
30783
Prove inequality $n<3^n$ using mathematical induction
48333
Prove by induction that $(x+1)^n - nx - 1$ is divisible by $x^2$
155897
Proof by induction - is this correct?
2197
Induction principle for $n!<n^n$
90789
Use induction to prove that that $8^{n} | (4n)!$ for all positive integers $n$
27304
Proving $ 1+\frac{1}{4}+\frac{1}{9}+\cdots+\frac{1}{n^2}\leq 2-\frac{1}{n}$ for all $n\geq 2$ by induction
55266
Prove that $(n+1)^{n-1}<n^n$
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Proof by Induction: $\sum_0^nx^i=(1-x^{n+1})/(1-x)$
52427
Prove, $\sqrt{n} \le (n!)^\frac{1}{n} \le \frac{n+1}{2} $
138683
Proving $\prod_{i=2}^{i=n} \left(1-\frac{1}{i^2}\right) = \frac{n+1}{2n}$ by induction