2.3 Pascal’s Triangle

This time we put integers at the left, as we did before but also along the top

Thus we set A3 to \(0\) and A4 to =A3+1 and copy A4 down to A13. We set C1 to \(0\) and D1 to =C1+1 and copy D1 to the right to M1.

Now, we set C3 to be =B2+C2. Copy C2 (using Ctrl c). Select the rectangle from C3 to M13. Paste in the rectangle (using Ctrl v). (By the way there are icons near the top left for copying and pasting that you can use instead of using the Ctrl c or Ctrl v.)

What do you see? You should see all \(0\)'s.

Now set C3 to be \(1\). You should now see a slanted Pascal triangle bordered by \(1\)'s in the selected area.

The content of any selected box is the binomial coefficient \(C(n,k)\) or \(\frac{n!}{k!(n-k)!}\) where \(n\) is the number in the A column of the box and \(k\) is the one in its first row.

Show table

We shall next see how we can use a spreadsheet to calculate areas.