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Know

uyslry2025 — 2025-05-20 17:06:48 UTC

Each row ofthe Pascal triangle represents a binomial expansion (A+ b)a coefficient in n, where n is the line number (counting from 0).

For example, line 0 represents (a + b)', line 1 represents (a + b), and so on.Each number is the sum oftwo numbers right above it, and except forthe first and last digits in each line, they are always 1.

How to build?

uyslry2025 — 2025-05-20 17:08:45 UTC

Step1:Write the number 1 at the top of the triangle.

which is row 0.

Step2 :Both ends of each line are 1. For other positionsin the line, each number is the sum of the twonumbers above it.

Step3 :Repeat step 2 and keep building the next lineuntil you reach the desired number oflines.

The relotionship between binomiol theorem ond Poscaltriangle

uyslry2025 — 2025-05-20 17:11:02 UTC

Example1

uyslry2025 — 2025-05-20 17:12:22 UTC

How do we find the fifth column of the Pascaltriongle?

The 5th line corresponds to n =4 (because the line numberstarts from 0).Calculate C(4, 0) to C(4, 4):

C(4,0)=C(4,4)=1

C(4,1)=C(4, 3)=4

C(4,2)=6

Therefore, line 5 is 1,4,6,4,1

Example2

uyslry2025 — 2025-05-20 17:14:03 UTC