pascal's triangle

[pugz519]

I am trying to solve two problems using Pascal's triangle but can't figure them out. Any help would be appreciated.

1. Starting with the second row from the top of Pascal's triangle, what is the sequence of the diagonal (1 2 3 4 5 6 7 )?

2. The sum of each row represents 2ⁿ , starting with the first row, which is 2⁰=1. Write an exponential expression for the sum of the values in the sixth row. Simplify the expression. (the sixth row shows (1 5 10 10 5 1 ) ).


Thanks

 

[pugz519]

PT

I think I may have started to figure out the second problem. Do I add up the numbers and put the total in exponential form with 2 on the bottom?

 

[pugz519]

The first question I am still not sure about but I think they may just be asking about the pattern of that diagonal. That the sequence is +1 to each number above it. For the second question I thought it ment this: 1+5+10+10+5+1=32=2^5. Does that make sense?

 

[pugz519]

Thanks for all your help.

 

[hotelsindanang]

How Pascal's Triangle is Constructed

At the tip of Pascal's Triangle is the number 1, which makes up the zeroth row. The first row (1 & 1) contains two 1's, both danang hotels formed by adding the two numbers above them to the left and the right, in this case 1 and 0 (all numbers outside the Triangle are 0's). Do the same to create the 2nd row: 0+1=1; 1+1=2; 1+0=1. And the third: 0+1=1; 1+2=3; 2+1=3; 1+0=1. In this way, the rows of the triangle go on infinitly. A number in the triangle can also hotels in da nang be found by nCr (n Choose r) where n is the number of the row and r is the element in that row. For example, in row 3, 1 is the zeroth element, 3 is element number 1, the next three is the 2nd element, and the last 1 is the 3rd element. The formula for nCr is: n! -------- r!(n-r)!

! means factorial, or the preceeding number multiplied by all the positive integers that are smaller than the number. 5! = 5 × 4 × 3 × 2 × 1 = 120.