Sierpinski's Triangle - 3

Geometry Level 2

This problem is part of a set of problems, please see the linked first problem , if you haven't yet.

Question: What is the area of the white triangles in Sierpinski's triangle at step n in its simplest form?

See the next problem .

Note: This problem is part of a set of problems, further investigating Sierpinski's Triangle in different ways. If you want to continue investigating click here . Questions will increase in difficulty.

Image Credits: Sierpinski's Triangle Image created by William Andrus. Removed grey outline.

1 − ( 3 4 ) n 1-(\frac{3}{4})^{n} None of these. ( 1 4 ) n (\frac{1}{4})^{n} ( 1 4 ) n × 3 n − 1 (\frac{1}{4})^{n} \times 3^{n-1} ( 3 4 ) n (\frac{3}{4})^{n} 1 − ( 1 4 ) n × 3 n − 1 1-(\frac{1}{4})^{n} \times 3^{n-1}

Ron Lauterbach by Ron Lauterbach , 18, Germany

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