15 Answered Questions
[SOLVED] Proof of the Hockey-Stick Identity: $\sum\limits_{t=0}^n \binom tk = \binom{n+1}{k+1}$
- 2015-10-21 14:46:44
- hlapointe
- 9279 View
- 49 Score
- 15 Answer
- Tags: discrete-mathematics summation binomial-coefficients combinations faq
31 Answered Questions
[SOLVED] Sum of First $n$ Squares Equals $\frac{n(n+1)(2n+1)}{6}$
- 2011-06-27 23:05:57
- Nathan Osman
- 61822 View
- 120 Score
- 31 Answer
- Tags: sequences-and-series discrete-mathematics summation
9 Answered Questions
[SOLVED] How to compute the formula $\sum \limits_{r=1}^d r \cdot 2^r$?
- 2010-11-23 05:52:25
- q0987
- 2601 View
- 8 Score
- 9 Answer
- Tags: calculus sequences-and-series discrete-mathematics summation
5 Answered Questions
[SOLVED] Can $\sqrt{n} + \sqrt{m}$ be rational if neither $n,m$ are perfect squares?
- 2013-08-01 16:42:42
- Spine Feast
- 3624 View
- 31 Score
- 5 Answer
- Tags: number-theory discrete-mathematics irrational-numbers rationality-testing faq
6 Answered Questions
[SOLVED] Questions on "All Horse are the Same Color" Proof by Complete Induction
- 2013-06-24 08:53:27
- MVTC
- 19758 View
- 32 Score
- 6 Answer
- Tags: discrete-mathematics induction fake-proofs
3 Answered Questions
[SOLVED] Mod of numbers with large exponents
- 2016-11-28 00:24:40
- Roshnal
- 1243 View
- 4 Score
- 3 Answer
- Tags: elementary-number-theory discrete-mathematics modular-arithmetic
8 Answered Questions
[SOLVED] Fibonacci addition law $F_{n+m} = F_{n-1}F_m + F_n F_{m+1}$
- 2010-11-23 07:15:38
- ghshtalt
- 4876 View
- 20 Score
- 8 Answer
- Tags: discrete-mathematics fibonacci-numbers
6 Answered Questions
[SOLVED] Using proof by contradiction vs proof of the contrapositive
- 2012-12-20 19:01:31
- Kasper
- 65886 View
- 132 Score
- 6 Answer
- Tags: discrete-mathematics logic propositional-calculus
6 Answered Questions
[SOLVED] Why is mathematical induction a valid proof technique?
- 2015-02-08 20:11:31
- Ali.B
- 9820 View
- 26 Score
- 6 Answer
- Tags: discrete-mathematics logic induction philosophy
6 Answered Questions
[SOLVED] Number of occurrences of k consecutive 1's in a binary string of length n (containing only 1's and 0's)
- 2016-12-05 21:26:07
- Armen Vardanyan
- 2386 View
- 4 Score
- 6 Answer
- Tags: sequences-and-series combinatorics discrete-mathematics
5 Answered Questions
[SOLVED] Sum with binomial coefficients: $\sum_{k=0}^{n}{2n\choose 2k}$
- 2012-03-31 17:23:20
- xan
- 2647 View
- 4 Score
- 5 Answer
- Tags: discrete-mathematics summation binomial-coefficients
4 Answered Questions
[SOLVED] Let $A$ be any uncountable set, and let $B$ be a countable subset of $A$. Prove that the cardinality of $A = A - B $
- 2013-04-08 17:30:09
- nicefella
- 5139 View
- 6 Score
- 4 Answer
- Tags: elementary-set-theory discrete-mathematics cardinals
2 Answered Questions
[SOLVED] Show that $n$ lines separate the plane into $\frac{(n^2+n+2)}{2}$ regions
- 2012-10-09 05:36:35
- Bob John
- 9856 View
- 14 Score
- 2 Answer
- Tags: discrete-mathematics logic induction
2 Answered Questions
[SOLVED] Counting number of moves on a grid
- 2010-11-27 18:33:02
- Snowman
- 6288 View
- 9 Score
- 2 Answer
- Tags: combinatorics discrete-mathematics permutations
5 Answered Questions
[SOLVED] How many distinct functions can be defined from set A to B?
- 2012-10-29 03:33:43
- imkendal
- 100961 View
- 29 Score
- 5 Answer
- Tags: combinatorics discrete-mathematics summation
5 Answered Questions
[SOLVED] Proving prime $p$ divides $\binom{p}{k}$ for $k\in\{1,\ldots,p-1\}$
- 2013-03-12 17:52:48
- user66463
- 12599 View
- 16 Score
- 5 Answer
- Tags: elementary-number-theory discrete-mathematics binomial-coefficients divisibility
5 Answered Questions
[SOLVED] $A \oplus B = A \oplus C$ imply $B = C$?
- 2013-10-23 17:32:48
- mathis...Math
- 1804 View
- 8 Score
- 5 Answer
- Tags: elementary-set-theory discrete-mathematics proof-writing
6 Answered Questions
[SOLVED] General formula for the 1; 5; 19; 65; 211 sequence
- 2016-05-18 16:52:46
- Olimjon
- 7007 View
- 6 Score
- 6 Answer
- Tags: sequences-and-series discrete-mathematics
4 Answered Questions
[SOLVED] Prove $\binom{n}{a}\binom{n-a}{b-a} = \binom{n}{b}\binom{b}{a}$
- 2013-10-21 06:44:28
- More Code
- 612 View
- 8 Score
- 4 Answer
- Tags: combinatorics discrete-mathematics binomial-coefficients
3 Answered Questions
[SOLVED] How to get the correct angle of the ellipse after approximation
- 2016-06-25 18:29:25
- Qulery
- 383 View
- 3 Score
- 3 Answer
- Tags: calculus ordinary-differential-equations discrete-mathematics conic-sections quadratics
5 Answered Questions
[SOLVED] Proving $ 1+\frac{1}{4}+\frac{1}{9}+\cdots+\frac{1}{n^2}\leq 2-\frac{1}{n}$ for all $n\geq 2$ by induction
- 2015-04-04 19:29:06
- Donald Dang
- 10863 View
- 2 Score
- 5 Answer
- Tags: discrete-mathematics inequality summation induction
5 Answered Questions
[SOLVED] Show that if $g \circ f$ is injective, then so is $f$.
- 2015-05-10 00:43:24
- thisisourconcerndude
- 6138 View
- 13 Score
- 5 Answer
- Tags: functions discrete-mathematics proof-writing
4 Answered Questions
[SOLVED] Prove by Mathematical Induction: $1(1!) + 2(2!) + \cdot \cdot \cdot +n(n!) = (n+1)!-1$
- 2013-02-12 22:16:42
- rbtLong
- 13643 View
- 7 Score
- 4 Answer
- Tags: discrete-mathematics summation induction factorial
3 Answered Questions
[SOLVED] Prove $f(S \cup T) = f(S) \cup f(T)$
- 2012-11-06 03:12:00
- George Milton
- 2343 View
- 5 Score
- 3 Answer
- Tags: functions elementary-set-theory discrete-mathematics
2 Answered Questions
[SOLVED] Coupon Collector Problem with Batched Selections
- 2012-04-14 09:44:12
- rukh
- 1890 View
- 2 Score
- 2 Answer
- Tags: probability combinatorics discrete-mathematics coupon-collector
4 Answered Questions
[SOLVED] Sum of cubes proof
- 2014-10-14 12:56:46
- hchenn
- 16258 View
- 4 Score
- 4 Answer
- Tags: discrete-mathematics proof-writing
2 Answered Questions
[SOLVED] What exactly is the difference between weak and strong induction?
- 2015-03-10 23:23:14
- Al Jebr
- 27405 View
- 21 Score
- 2 Answer
- Tags: discrete-mathematics logic proof-writing induction
2 Answered Questions
[SOLVED] Choosing numbers without consecutive numbers.
- 2013-09-11 09:40:29
- NightRa
- 12649 View
- 11 Score
- 2 Answer
- Tags: combinatorics discrete-mathematics
2 Answered Questions
[SOLVED] Prove that $\mathcal{P}(A)⊆ \mathcal{P}(B)$ if and only if $A⊆B$.
- 2013-03-16 17:42:32
- Mack
- 15730 View
- 13 Score
- 2 Answer
- Tags: discrete-mathematics proof-writing
8 Answered Questions
[SOLVED] What is $\gcd(0,0)$?
- 2013-09-16 04:53:59
- Konstantin Weitz
- 15267 View
- 67 Score
- 8 Answer
- Tags: elementary-number-theory discrete-mathematics divisibility gcd-and-lcm