What is pascal triangle

Question

i dont understand the pascal law at all.

Answer 1

It is a triangular array showing the coefficients of a binomial elevated to a power.  Consider (x + y)ⁿ.

 

n = 0:

(x + y)⁰ = 1

 

n = 1:

(x + y)¹ = x + y

 

n = 2:

(x + y)² = x² + 2xy + y²

 

n = 3:

(x + y)³ = x³ + 3x²y + 3xy² + y³

 

Note if we stack the coefficients in rows starting with n = 0 at the top, we get

 

   1

  1 1

 1 2 1

1 3 3 1

.

.

.

etc.

 

Each row starts with 1 and ends with 1.  Any other coefficient in a particular row is the sum of its two neighbors in the row above.  It is a convenient way to get the coefficients of a binomial expansion without having to explicitly perform the multiplications, remembering that the first term has xⁿy⁰, with the power of x decreasing by 1 and the power of y increasing by 1 until the last term has x⁰yⁿ.