Pascal's Triangle and the Binomial Theorem
Pascal's Triangle and the Binomial Theorem
This Demonstration illustrates the direct relation between Pascal's triangle and the binomial theorem. This very well-known connection is pointed out by the identity =
+
b+
+…+
a+
,n∈, where the binomial coefficients can be obtained by using Pascal's triangle.
n
(a+b)
n |
0 |
n
a
n |
1 |
n-1
a
n |
2 |
n-2
a
2
b
n |
n-1 |
n-1
b
n |
n |
n
b