Question
The sum of the numbers in the $n$ th row of Pascal's Triangle is $2^{n}$.
Step 1
So, let's write down the expansion: \[(x+y)^n = \binom{n}{0}x^n + \binom{n}{1}x^{n-1}y + \binom{n}{2}x^{n-2}y^2 + \ldots + \binom{n}{n}y^n\] Show more…
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Key Concepts
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a) Determine the sum of the numbers in each of the first five rows in Pascal's triangle. b) What is an expression for the sum of the numbers in the ninth row of Pascal's triangle? c) What is a formula for the sum of the numbers in the $n$ th row?
Permutations, Combinations, and the Binomial Theorem
Binomial Theorem
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