how to draw pascal triangle ?

Question

how to draw pascal triangle ?

i forget it very easily .

can you please help me to remember it ?

can you please tell me any tricks / mnemonic ?

tell me some tricks which will help me to remember it always.

thanks

Answer 1

..........1
........1...1
......1...2...1
....1...3...3...1
..1...4...6...4...1
1..5..10..10..5...1
etc.

Each row starts and ends with 1.
Every other number is the sum of the two numbers directly above it.
And if you want to reproduce a certain row, without building the entire triangle, the formula for the entries is:

n!/[(n-k)!k!]
where n! (n factorial) = n*(n-1)*(n-2)*...*3*2*1

Where n is the n-th row and k is the k-th term in the row.

(Here, the very first row, the one with just "1", is considered the 0th row, and in every row, the "1" at the beginning is considered the 0-th term in the row.)

So, for example, the 3rd term in the 10th row is:
10!/[(10-3)!3!]
= 10!/(7! * 3!)
= 10*9*8 / (3*2*1)
= 120

(The 10th row is:
1, 10, 45, 120, 210, 256, 210, 120, 45, 10, 1)

Answer 2

Each line starts and ends with a 1. Other numbers are sum of two numbers above it.

1
1 1
1 2 1
1 3 3 1
1 4 6 4 1

...

Answer 3

Start with 1 in the first row
1 1 in the second row
each number in the next row is the sum of two adjacent numbers in the row above. Imagine zeroes being on the end of the row.
So row 3 will be
1 2 1
row 4 will be 1 3 3 1. etc.

If you want a specific row or term you can use the binomial theorem

Answer 4

Easier to generate it: It start with 1 1. Every row has one more number than the previous row and all row begin and end with 1. The other numbers are the sum of the numbers above to the immediate left and right. Row 2: 1 2 1 Row 3: 1 3 3 1 Row 4: 1 4 6 4 1 Etc. If you know combination notation, row 5: C(5,0) C(5,1) C(5,2) C(5,3) C(5,4) C(5,5)

Answer 5

first three lines:
1
11
121 ---- All you do is add the two numbers above together
1331 so for the next one, you would have one's on the outside and then add the other ones so:
14641


I don't know if this helped. I don't really know how to explain it without showing you. :S