00:01
This problem says what is the sum of the numbers in the 14th row of pascal's triangle? and when we are creating pascal's triangle, we start off with a 1 at the top of the triangle, and then we have 1 and 1 for our first row, and then 1 -2 -1 for our next row.
00:18
And then we see the pattern where we start with the 1, add the numbers above for our next entry, so 1 plus 2 gives us 3, 2 plus 1 gives us 3, and then finish with a 1.
00:27
And then we would continue this pattern, and the 4th row would be 1.
00:30
1, 4, 6, 4, 1, and then so on and so forth.
00:36
But when we are looking at the 14th row that would take us a while to be able to draw out the entire pascal's triangle and then find the sum.
00:42
So we're going to see if we can find a pattern to be able to find the sum without having to draw up the entire triangle.
00:49
And the first row would be our 1 -1, which would sum to give us 2.
00:53
Our second row after the first row would be 1 plus 2 plus 1, which would give us 4.
00:59
Our third row would be 1 plus 3 plus 3 plus 1, which would give us 8.
01:05
Our fourth row, which would be 1 plus 4 plus 6 plus 4 plus 1, would give us 16...