Premium Only Content

Pascal's triangle: and expansion of formulas and application exercise
Pascal's Triangle is a mathematical tool used to calculate binomial and combinatorial coefficients. It is named after the French mathematician Blaise Pascal.
Structure of Pascal's Triangle
The triangle is constructed as follows:
1. The first row has a 1.
2. Each subsequent row begins and ends with a 1.
3. The other numbers are calculated by adding the two numbers directly above.
Example of Pascal's Triangle
```
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
```
Formula to calculate a number in Pascal's Triangle
The number in row n and column k is calculated with the formula:
C(n, k) = n! / (k!(n-k)!)
where:
1. n is the row number
2. k is the column number
3. ! denotes the factorial (product of all positive integers up to that number)
Applications of Pascal's Triangle
1. Calculation of binomial coefficients
2. Combinatorics
3. Probability
4. Statistics
5. Algebra
6. Geometry
Properties of Pascal's Triangle
1. Symmetry
2. The sum of the numbers in each row is a power of 2
3. The sum of the numbers in each column is a power of 2
4. The triangle is used in the expansion of the binomial theorem.
-
10:47
Nikko Ortiz
16 hours ago15 Seconds Of Fame Gone WRONG...
108K11 -
14:47
GritsGG
1 day agoRumble Tournament Dubular! Rebirth Island Custom Tournament!
69.9K5 -
1:36:05
Side Scrollers Podcast
19 hours agoStreamer ATTACKS Men Then Cries Victim + Pronoun Rant Anniversary + More | Side Scrollers
80.4K4 -
LIVE
Lofi Girl
2 years agoSynthwave Radio 🌌 - beats to chill/game to
266 watching -
42:55
Stephen Gardner
1 day ago🔥Trump’s SURPRISE Move STUNS Everyone - Democrats PANIC!
102K123 -
1:37:19
Badlands Media
16 hours agoBaseless Conspiracies Ep. 148: The Delphi Murders – Secrets, Setups, and Cover-Ups
47.1K17 -
5:59:05
SpartakusLIVE
10 hours ago#1 MACHINE Never Stops The GRIND || LAST Stream UNTIL Friday
152K2 -
28:36
Afshin Rattansi's Going Underground
1 day agoDoug Bandow: ENORMOUS DAMAGE Done to US’ Reputation Over Gaza, Trump ‘Easily Manipulated’ by Israel
33.4K34 -
2:45:13
Barry Cunningham
17 hours agoCBS CAUGHT AGAIN! CHICAGO A MESS! LISA COOK IS COOKED AND MORE LABOR DAY NEWS!
122K51 -
6:39:17
StevieTLIVE
11 hours agoMASSIVE Warzone Wins on Labor Day w/ Spartakus
37.9K1