In pascal's triangle, which row has the sum of 524288?
The nth row sums to 2^(n-1), so which power of 2 = 524288?
log2524288 = 19
so the 20th row is the one.
thanks.
16
To find the row in Pascal's triangle that has a sum of 524288, you can add up the numbers in each row sequentially until you reach the desired sum.
Pascal's triangle can be easily generated by adding the two numbers above each number in the triangle. The first row is always 1, and each subsequent row is constructed by adding the adjacent numbers from the row above.
Here's an example of Pascal's triangle:
```
Row 1: 1
Row 2: 1 1
Row 3: 1 2 1
Row 4: 1 3 3 1
Row 5: 1 4 6 4 1
```
Starting with the first row, you can add the numbers in each row until you reach the sum of 524288.
Row 1: 1 = 1
Row 2: 1 + 1 = 2
Row 3: 1 + 2 + 1 = 4
Row 4: 1 + 3 + 3 + 1 = 8
Row 5: 1 + 4 + 6 + 4 + 1 = 16
Row 6: 1 + 5 + 10 + 10 + 5 + 1 = 32
Row 7: 1 + 6 + 15 + 20 + 15 + 6 + 1 = 64
Row 8: 1 + 7 + 21 + 35 + 35 + 21 + 7 + 1 = 128
Row 9: 1 + 8 + 28 + 56 + 70 + 56 + 28 + 8 + 1 = 256
Row 10: 1 + 9 + 36 + 84 + 126 + 126 + 84 + 36 + 9 + 1 = 512
Row 11: 1 + 10 + 45 + 120 + 210 + 252 + 210 + 120 + 45 + 10 + 1 = 1024
As you can see, the sum of the numbers in Row 10 is 512, and the sum of the numbers in Row 11 is 1024. Therefore, the sum of 524288 is not present in the first 10 rows of Pascal's triangle.
You would need to continue adding the numbers in each row until you find the row with a sum of 524288. However, since Pascal's triangle is infinite, there is no definitive end to the rows.