Q: What is the sum of the numbers in the seventh row of pascal s triangle?

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The sum of the numbers on the fifteenth row of Pascal's triangle is 215 = 32768.

1 6 15 20 15 6 1

The rth term of the 25th row is 25!/[r!(25-r)!] where r = 0,1,2,...,25 and k! denotes 1*2*3*...*k and 0! = 1 So 1 25 300 2,300 12,650 53,130 177,100 480,700 1,081,575 2,042,975 3,268,760 4,457,400 5,200,300 and then the same numbers in reverse order, all the way back to 1.

1 20 190 1140 4845 15504 38760 77520 125970 167960 184756 167960 125970 77520 38760 15504 4845 1140 190 20 1

1 21 210 1330 5985 20349 54264 116280 203490 293930 352716 352716 293930 203490 116280 54264 20349 5985 1330 210 21 1

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The sum of the numbers on the fifteenth row of Pascal's triangle is 215 = 32768.

The sum of the numbers in each row of Pascal's triangle is twice the sum of the previous row. Perhaps you can work it out from there. (Basically, you should use powers of 2.)

4

The number of odd numbers in the Nth row of Pascal's triangle is equal to 2^n, where n is the number of 1's in the binary form of the N. In this case, 100 in binary is 1100100, so there are 8 odd numbers in the 100th row of Pascal's triangle.

The Fifth row of Pascal's triangle has 1,4,6,4,1. The sum is 16.

If you consider row 0 as the row consisting of the single 1, then row 100 has 6 odd numbers.

1 6 15 20 15 6 1

It is 2n, if that is what you were trying to ask.

The numbers are 100Cn = 100!/[n!*(100-n)!] for n = 0, 1, ... , 100

When evaluating row n+1 of Pascal's triangle, each number from row n is used twice: each number from row ncontributes to the two numbers diagonally below it, to its left and right. From this it is easily seen that the sum total of row n+1 is twice that of row n. The first row of Pascal's triangle, containing only the single '1', is considered to be row zero. Its total, 1, is given by 20. From the above observations, we can conclude that the total of row n is given by 2n. For the eleventh row: 211 = 2048.

The sum of the 20th row in Pascal's triangle is 1048576.

Each element of a row of pascal's triangle is the sum of the two elements above it. Therefore when you some the elements of a row, each of the elements of the row above are being summed twice. Thus the sum of each row of pascal's triangle is twice the sum of the previous row.