Name: Applications of Pascal's Triangle
Uploaded: 2019-07-19
Duration: 3 min 57 s
Description: What does the inside of a tesseract look like? Pascal's Triangle can tell us. Watch this video to know more about Applications of Pascal's Triangle

Question

Can row sum of elements in a Pascal's Triangle form a pattern?

Accepted Answer

First row $= 2^{1 - 1} = 1$
Second row $= 2^{2 - 1} = 2 \times 1 = 2$
Third row $= 2^{3 - 1} = 2 \times 2 = 4$
Fourth row $= 2^{4 - 1} = 2 \times 2 \times 2 = 8$
Fifth row $= 2^{5 - 1} = 2 \times 2 \times 2 \times 2 = 16$
Sixth row $= 2^{6 - 1} = 2 \times 2 \times 2 \times 2 \times 2 = 32$
Seventh row $= 2^{7 - 1} = 2 \times 2 \times 2 \times 2 \times 2 \times 2 = 64$
Eighth row $= 2^{8 - 1} = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 = 128$

Here x denotes the row and y denotes the corresponding row sum. The values of x and y can be tabulated as follows:

$X$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ ...

$Y$ $1$ $2$ $4$ $8$ $16$ $32$ $64$ $128$ ...

The relationship between x and y is $y = 2^{x - 1}$ .

Can row sum of elements in a Pascal's Triangle form a pattern?

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