List questions from induction

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Prove By Induction (Fibonacci Sequence)

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Function composition: $f^{653}(56)=?$

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Inductive proof of the degree of a polynomial

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Combinatorics identity proof by induction

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Prove by mathematical induction that exponentials grow faster than polynomials

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Inductive proof of the identity $\binom{n} {0} F_0+\binom{n}{1} F_1+\binom{n}{2} F_2+\cdots +\binom{n}{n} F_n=F_{2n}$

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characteristic function differentiation

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Use Induction to prove: $(1+2x)^n \geq 1+2nx$

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Proving that if one person in any group of four knows three, then someone knows everyone.

Published on 25 Oct 2014 - 16:25

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Prove by induction that $r_0 + r_1a + r_2a^2 + \cdots + r_{n−1}a^{n−1} < a^n$.

Published on 26 Oct 2014 - 6:14

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Proof by induction with variable other than $n$

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How can I show that $n! \leqslant \left(\frac{n+1}{2}\right)^n$?

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Proving inequality $4n<2^n$ using induction all natural numbers that's greater than or equal to 5

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Prove that if $n^2$ is divided by 3, then also $n$ can also be divided by 3.

Published on 01 Apr 2026 - 9:53

List Question

Number of particles at time $t$

Prove By Induction (Fibonacci Sequence)

Function composition: $f^{653}(56)=?$

Inductive proof of the degree of a polynomial

Combinatorics identity proof by induction

Prove by mathematical induction that exponentials grow faster than polynomials

Inductive proof of the identity $\binom{n} {0} F_0+\binom{n}{1} F_1+\binom{n}{2} F_2+\cdots +\binom{n}{n} F_n=F_{2n}$

characteristic function differentiation

Use Induction to prove: $(1+2x)^n \geq 1+2nx$

Proving that if one person in any group of four knows three, then someone knows everyone.

Prove by induction that $r_0 + r_1a + r_2a^2 + \cdots + r_{n−1}a^{n−1} < a^n$.

Proof by induction with variable other than $n$

How can I show that $n! \leqslant \left(\frac{n+1}{2}\right)^n$?

Proving inequality $4n<2^n$ using induction all natural numbers that's greater than or equal to 5

Prove that if $n^2$ is divided by 3, then also $n$ can also be divided by 3.

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