List questions from induction

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Prove by induction that $4n^2 + 1 < 3\cdot 2^n$ for every $n \ge 6$

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Prove that $\operatorname{fib}(n)$ is the closest integer to $\frac{\phi^{n}}{\sqrt{5}}$

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Prove by induction on $n\geq1$ that $f^{(n)}(x)=n!a_n(1+x)^{\frac{1}{2}-n}$ for all $x\in(-1,\infty)$

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Proof By Induction: $\sum_{i=1}^n \frac{1}{\sqrt i} > \sqrt n$

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Given $x_1 \colon=1$, $x_2 \colon=2$, and $x_n\colon=\left( x_{n-1}+x_{n-2}\right)/2$, how to establish this relation?

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Graphs, at-most-one-intermediate paths and induction

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Prove the following inequality by Induction

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List Question

Logic in Computer Science - Define inclusive XOR by induction

How to prove a sequence is strictly increasing and bounded above?

Explanation of inequality proof

Proving Inequalities With Mathematical Induction

Prove by induction that $4n^2 + 1 < 3\cdot 2^n$ for every $n \ge 6$

Proof by induction with factorials

Prove that $\operatorname{fib}(n)$ is the closest integer to $\frac{\phi^{n}}{\sqrt{5}}$

Prove by induction on $n\geq1$ that $f^{(n)}(x)=n!a_n(1+x)^{\frac{1}{2}-n}$ for all $x\in(-1,\infty)$

Proof By Induction: $\sum_{i=1}^n \frac{1}{\sqrt i} > \sqrt n$

Given $x_1 \colon=1$, $x_2 \colon=2$, and $x_n\colon=\left( x_{n-1}+x_{n-2}\right)/2$, how to establish this relation?

Graphs, at-most-one-intermediate paths and induction

Prove the following inequality by Induction

Solving an inequality induction

Classical examples of mathematical induction

To prove the equivalence of the induction principles, why does it seems we assume what we want to prove?

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