Need help with Pascals triangle?

Question

Need help with Pascals triangle?
1.can you predict the number of binomial coefficients when n is 100.
2.How many ones are there in the 21st row of Pascals triangle?explain your answer.
3.What is the rule of how the Pascal triangle is constructed...
4what would happen if the second ellement in a row is a prime number.what can you say about other numbers in that row?

if you can answer any of those questions then you are a genius because i cannot understand one thing here.
thanks

Answer 1

1. 101
2. There are 2 ones. The first and last entries of the row.
3. Each entry is the sum of the 2 entries above and to each side of it.
4. If the 2'nd entry in a row is a prime, it divides each of the other entries in the row (except for the last entry in the row which is always a 1)

Check out http://ptri1.tripod.com/ for all manner of kewl sh|t about Pascal's Triangle. Also Fibonacci Series and other fun things ☺


Doug

EDIT: Give Peter D the points. He needs 'em worse than I do ☺

Answer 2

n k →
↓
0. . . . . . . . . . . . . . .1
1 . . . . . . . . . . . . . 1. 1
2. .. . .. . . . . . . . .1. 2 . 1
. . . . . . . . . . . . .1. 3 . 3 . 1
. . . . . . . . . . . .1. .4. 6. .4. 1
. . . . . . . . . . .1. .5.10.10. 5 .1
6. . . . . . . . .1.. 6.15.20 15 6. 1

1) you can see the number of binomial coefficients is n+1 so for n=100 there will be 101 elements

2) 22 the answer is given in 1)


3)It's easy to construct the triangle of Pascal,
you see the number under two other numbers is the sum of these numbers.

4) the will be at least one more prime number

Answer 3

1. 100
2. 21, always as many numbers in a row (i.e. coefficients) as the row number
3.


start with 1
next row: 1 1
next rows: write between each number in the prev. row the sum of them. So:
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
1 6 15 20 15 6 1
...

4. the second element is always equal to the row number/number of elements in this row, so if that is a prime, than the number of elements in that row is also a prime.

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