Question

Prove that $\frac23 + \frac29 + \dots + \frac{2}{3^n} = 1 - \left( \frac13 \right) ^n$

score 110 · Answer 1 · 2016-09-18 09:30:39

110

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Prove that $\frac23 + \frac29 + \dots + \frac{2}{3^n} = 1 - \left( \frac13 \right) ^n$

Published on 18 Sep 2016 - 9:30

score 1.6k · Answer 2 · 2016-09-18 13:20:05

1.6k

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Prove by induction that a circle cut by $n$ chords can be filled by 2 colors in a way that adjacent regions differ in color

Published on 18 Sep 2016 - 13:20

score 907 · Answer 3 · 2026-03-30 02:11:29

907

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Integers $n$ such that $n^2$ is of the form $3k+2$

Published on 30 Mar 2026 - 2:11

score 56 · Answer 4 · 2026-04-01 04:39:47

56

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Proof that recursion $U_0 = 0$, $U_n= 1 + U_\left \lfloor n/2 \right \rfloor$, is solved by $U_n = \left \lfloor \log_2(n) \right \rfloor + 1$

Published on 01 Apr 2026 - 4:39

score 371 · Answer 5 · 2016-09-18 15:41:43

371

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Prove that for a positive number only exists one natural number such that $b{++} = a$

Published on 18 Sep 2016 - 15:41

score 1.2k · Answer 6 · 2016-09-18 17:34:36

1.2k

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Proof by induction: the $n$-th derivative $f^{(n)}$ of function $f(x)=xe^{x-1}$ is same as ...

Published on 18 Sep 2016 - 17:34

score 553 · Answer 7 · 2026-04-13 08:18:12

553

Views

Proving $n^2 \leq 2^n$ using simple induction

Published on 13 Apr 2026 - 8:18

score 741 · Answer 8 · 2026-03-29 05:44:09

741

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How to apply 1st Isomorphism Theorem to show that a finite abelian group has a subgroup of order $n$ for each positive divisor $n$ of its order

Published on 29 Mar 2026 - 5:44

score 132 · Answer 9 · 2016-09-19 15:29:45

132

Views

Proving $\sum_{i=1}^{n} i^2$ via mathematical induction

Published on 19 Sep 2016 - 15:29

score 40 · Answer 10 · 2026-04-10 16:38:06

40

Views

mathmatical induction of fibonacci sequence supporting questions

Published on 10 Apr 2026 - 16:38

score 815 · Answer 11 · 2026-04-12 22:22:00

815

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Proof by induction: $2^{n} < n!$

Published on 12 Apr 2026 - 22:22

score 1k · Answer 12 · 2016-09-21 04:32:11

1k

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If $A$ is finite and $B\subset A$, then $B$ is finite

Published on 21 Sep 2016 - 4:32

score 347 · Answer 13 · 2016-09-21 07:49:51

347

Views

Show that $m! (n − m)!$ divides $n!$ for all $m$, $n \in \Bbb{N}$ with $m \leq n$.

Published on 21 Sep 2016 - 7:49

score 99 · Answer 14 · 2016-09-21 09:43:16

99

Views

Prove by induction

Published on 21 Sep 2016 - 9:43

score 674 · Answer 15 · 2026-03-31 08:12:05

674

Views

$K$ field of characteristic $p$, where $p$ is prime

Published on 31 Mar 2026 - 8:12

List Question

Prove that $\frac23 + \frac29 + \dots + \frac{2}{3^n} = 1 - \left( \frac13 \right) ^n$

Prove by induction that a circle cut by $n$ chords can be filled by 2 colors in a way that adjacent regions differ in color

Integers $n$ such that $n^2$ is of the form $3k+2$

Proof that recursion $U_0 = 0$, $U_n= 1 + U_\left \lfloor n/2 \right \rfloor$, is solved by $U_n = \left \lfloor \log_2(n) \right \rfloor + 1$

Prove that for a positive number only exists one natural number such that $b{++} = a$

Proof by induction: the $n$-th derivative $f^{(n)}$ of function $f(x)=xe^{x-1}$ is same as ...

Proving $n^2 \leq 2^n$ using simple induction

How to apply 1st Isomorphism Theorem to show that a finite abelian group has a subgroup of order $n$ for each positive divisor $n$ of its order

Proving $\sum_{i=1}^{n} i^2$ via mathematical induction

mathmatical induction of fibonacci sequence supporting questions

Proof by induction: $2^{n} < n!$

If $A$ is finite and $B\subset A$, then $B$ is finite

Show that $m! (n − m)!$ divides $n!$ for all $m$, $n \in \Bbb{N}$ with $m \leq n$.

Prove by induction

$K$ field of characteristic $p$, where $p$ is prime

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