Question

What is pascal's triangle. Explain with an example

Answer 1

The binomial theorem refers to the pattern of coefficients (numbers that appear in front of variables) that appear when a binomial is multiplied by itself a certain number of times. ... Pascal's triangle can be used to determine the expanded pattern of coefficients

See the Image First

We can find any element of any row using the combination function. The rth element of Row n is given by:

C(n, r - 1) =  

For example, the 3rd entry in Row 6 (r = 3, n = 6) is C(6, 3 - 1) = C(6, 2) =  = 15.

Examples  

What is the 5th entry in the Row 7 of Pascal's Triangle?

C(7, 4) =  = 35.

What is the 6th entry in Row 5 of Pascal's Triangle?

C(5, 5) =  = 1  

What is the 9th entry in Row 20 of Pascal's Triangle?

C(20, 8) =  = 125970

What is the 2nd entry in Row 103 of Pascal's Triangle?

C(103, 1) =  = 103