List questions from induction

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Prove by induction that $(1+x)^n \geq 1+nx$

Published on 19 Apr 2014 - 14:10

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Variation of Nim: Player who takes last match loses

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Proof by induction that $\sum_{j=0}^n 2^j = 2^{n+1} - 1$

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induction on matrices with powers + addition and limit

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A problem on mathematical induction

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Proving $\arctan1 + \arctan\frac13 +\cdots+\arctan\frac1{n^2+n+1}=\arctan (n+1)$ by induction

Published on 21 Apr 2014 - 9:35

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Proof by induction question about fuel depots

Published on 21 Apr 2014 - 11:03

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$a_1a_2\cdots a_n = 1 \implies a_1 + a_2 + \cdots + a_n \geq n$ if $a_1, a_2, \dots, a_n > 0$

Published on 21 Apr 2014 - 12:40

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Use of mathematical induction to compute $\int_0^{\pi/2} \sin^{2n+1}xdx$?

Published on 21 Apr 2014 - 16:36

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Hint in Proving that $n^2\le n!$

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Round robin algorithm proof

Published on 22 Apr 2014 - 18:46

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Everyone has brown eyes

Published on 24 Apr 2014 - 1:36

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Divisibility by induction

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A polynomial with integer coefficient

Published on 30 Mar 2026 - 10:07

List Question

Cauchy-Euler Equation of order $n$

Prove by induction that $(1+x)^n \geq 1+nx$

Variation of Nim: Player who takes last match loses

Proof by induction that $\sum_{j=0}^n 2^j = 2^{n+1} - 1$

induction on matrices with powers + addition and limit

A problem on mathematical induction

Proving $\arctan1 + \arctan\frac13 +\cdots+\arctan\frac1{n^2+n+1}=\arctan (n+1)$ by induction

Proof by induction question about fuel depots

$a_1a_2\cdots a_n = 1 \implies a_1 + a_2 + \cdots + a_n \geq n$ if $a_1, a_2, \dots, a_n > 0$

Use of mathematical induction to compute $\int_0^{\pi/2} \sin^{2n+1}xdx$?

Hint in Proving that $n^2\le n!$

Round robin algorithm proof

Everyone has brown eyes

Divisibility by induction

A polynomial with integer coefficient

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