a) What is Pascal’s triangle?
b) How can a row of Pascal’s triangle be produced from the one above it?
(a) A geometric arrangement of the binomial coefficients in a triangle which is based on Pascal's identity is known as Pascal’s triangle.
(b) A row of Pascal’s triangle can be produced from the one above it by using the formula .
Pascal's triangle is a triangular array of binomial coefficients found in probability theory, combinatorics, and algebra in mathematics.
Pascal's triangle is a geometric arrangement of the binomial coefficients in a triangle based on the principle called Pascal's identity which states that for. The row in the triangle consists of the binomial coefficients –
Therefore, Pascal triangle is based on Pascal’s identity .
The term in the row in Pascal's triangle is just the sum of the and terms in its above row, i.e., the row. Let be the term in the row of Pascal's triangle for then the row can be obtained as –
Therefore, the row can be obtained using the formula role="math" localid="1668683483371" .
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