Request a call back

Join NOW to get access to exclusive study material for best results

CBSE Class 9 Answered

what is the mathematics involved in a pascal triangle?
Asked by Vidisha | 12 Jun, 2013, 05:44: PM
answered-by-expert Expert Answer

In mathematics, Pascal's triangle is a triangular array of the binomial coefficients. It is named after the French mathematicianBlaise Pascal in much of the Western world, although other mathematicians studied it centuries before him in India, Greece,Iran, China, Germany, and Italy.

The rows of Pascal's triangle are conventionally enumerated starting with row n = 0 at the top. The entries in each row are numbered from the left beginning with k = 0 and are usually staggered relative to the numbers in the adjacent rows. A simple construction of the triangle proceeds in the following manner. On row 0, write only the number 1. Then, to construct the elements of following rows, add the number above and to the left with the number above and to the right to find the new value. If either the number to the right or left is not present, substitute a zero in its place. For example, the first number in the first row is 0 + 1 = 1, whereas the numbers 1 and 3 in the third row are added to produce the number 4 in the fourth row.

This construction is related to the binomial coefficients by Pascal's rule, which says that if

then

for any nonnegative integer n and any integer k between 0 and n. 

Pascal's triangle has higher dimensional generalizations. The three-dimensional version is called Pascal's pyramid or Pascal's tetrahedron, while the general versions are called Pascal's simplices.

Answered by | 13 Jun, 2013, 03:53: AM

Application Videos

CBSE 9 - Maths
Asked by bascaljoseph | 07 Feb, 2023, 01:27: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
Asked by yadavPriy000 | 06 May, 2021, 07:11: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
Asked by manugaur698 | 11 Sep, 2020, 04:30: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
Asked by deepakumaraiya200 | 30 Jun, 2020, 09:51: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
Asked by maddinenianr | 21 Mar, 2020, 03:48: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
Asked by prakash.sanyasi | 04 Jan, 2020, 05:09: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
Asked by kishor.kp14 | 15 Dec, 2019, 05:00: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
Asked by ravinderchoudhary0486 | 06 Dec, 2019, 10:59: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
Asked by suresh | 27 Nov, 2019, 09:21: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
Get Latest Study Material for Academic year 24-25 Click here
×