Prove that $1 + nx ≤ (1 + x)^n$ , for all real numbers $x > −1$ and integers $n ≥ 2$ by mathematical induction.
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Proof by induction of Bernoulli's inequality: $(1 + x)^n \geq 1 + nx$
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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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Prove by Induction : $n < 2^n$
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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 $x+\frac{1}{x}\in\mathbb{Z}$.
51730
How to prove this inequality $3^{n}\geq n^{2}$ for $n\geq 1$ with mathematical induction?
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How to Prove with Mathematical Induction $3^n > n^2$
66387
Prove $(x_1+.....+x_n)^2 \leq n(x_1^2 + .....+x_n^2)$
67527
Proof by Induction that $3^n ≥ 1+2^n$
2197
Induction principle for $n!<n^n$
123757
Proving a summation inequality with induction
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Proof By Induction of a Sum
33082
Proving $\sum_{i=0}^n 2^i=2^{n+1}-1$ by induction.
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Proof that $x^n+\frac{1}{x^n}\in \mathbb Z$ by complete induction
3043
Prove $n!>2^n$ for $n\geq4$ using induction.
32427
Basic mathematical induction regarding inequalities
96332
Prove by induction that $\sqrt[n+1]{n+1}<\sqrt[n]{n}$ for $n\ge 3$
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Math Induction Proof: $(1+\frac1n)^n < n$