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The entries in a certain row of Pascal's triangle are

1, n, ..., n, 1

 

The average of the entries in this row is 2.  Find n.

 Dec 5, 2022
 #1
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Since the average is small, we can safely assume that it is easy to find using trial and error.

Row 0's average is 1.

Row 1's average is 1.

Row 2's average is \(\dfrac43\)

Row 3's average is \(\dfrac84\) which is simply 2.

 

We are not done yet, though.

Row three consists of \(1,3,3,1 \),

so thus \(\boxed{n=3}\)

 Dec 5, 2022

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