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Chapter 7: Problem 46

Find the tenth row of Pascal's triangle.

Short Answer

Expert verified
The tenth row of Pascal's triangle is: \[1\;9\;36\;84\;126\;126\;84\;36\;9\;1\].

Step by step solution

01

Starting with row 1

The first row of Pascal's Triangle is: \[1\]
02

Generating the next row

To generate the next row, we start with 1 and add the two numbers above the desired entry to get the subsequent numbers. Repeat this process until you reach the end of the row and append 1. The second row is: \[1\;\;1\]
03

Continuing the process

Now we generate the following rows of Pascal's triangle using the same method: Row 3: \[1\;\;2\;\;1\] Row 4: \[1\;\;3\;\;3\;\;1\] Row 5: \[1\;\;4\;\;6\;\;4\;\;1\] Row 6: \[1\;\;5\;\;10\;\;10\;\;5\;\;1\] Row 7: \[1\;\;6\;\;15\;\;20\;\;15\;\;6\;\;1\] Row 8: \[1\;\;7\;\;21\;\;35\;\;35\;\;21\;\;7\;\;1\] Row 9: \[1\;\;8\;\;28\;\;56\;\;70\;\;56\;\;28\;\;8\;\;1\]
04

Finding the tenth row

Using the same process, we generate the tenth row of Pascal's triangle: Row 10: \[1\;\;9\;\;36\;\;84\;\;126\;\;126\;\;84\;\;36\;\;9\;\;1\] So the tenth row of Pascal's triangle is: \[1\;9\;36\;84\;126\;126\;84\;36\;9\;1\]

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Most popular questions from this chapter

Define a sequence recursively by \(a_{1}=6\) and \(a_{n+1}=\frac{1}{2}\left(\frac{17}{a_{n}}+a_{n}\right)\) for \(n \geq 1 .\) Find the smallest value of \(n\) such that \(a_{n}\) agrees with \(\sqrt{17}\) for at least four digits after the decimal point.

Express $$ 5.1372647264 \ldots $$ as a fraction; here the digits 7264 repeat forever.

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