The Fibonacci Sequence and the Binomial Theorem ...

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Pascal's TriangleHow many different patterns can you find in the triangle?

Pascal's TriangleCan you find the Fibonacci sequence in the triangle?

Any individual term, let's say the ith term, in a binomial expansion can be represented like this:

Example: Find the 4th term in the expansion of

Recall: This relation holds for each term in any binomial expansion:

Example: Find the term that contains x in the expansion of

[exponent on a] + [exponent on b] = n

And any individual term in a binomial expansion can be represented like this:

Recall: This relation holds for each term in any binomial expansion:

Example: Find the term that contains x in the expansion of

[exponent on a] + [exponent on b] = n

And any individual term in a binomial expansion can be represented like this:

Recall: This relation holds for each term in any binomial expansion:

Example: Find the term that contains x in the expansion of

[exponent on a] + [exponent on b] = n

And any individual term in a binomial expansion can be represented like this:

Example: Find the term that contains x in the expansion of 7

Determine the indicated term in each expansion.

(a) the 8th term in the expansion of

Determine the indicated term in each expansion.

(b) the 4th term in the expansion of

Determine the indicated term in each expansion.

(c) the middle term in the expansion of

Find the term that contains in the expansion of:

This question is HOMEWORKand Exercise #34.