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Q: How much is the sum of the numbers from the 20th row?

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16020

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.)

Each number in Pascal's triangle is used twice when calculating the row below. Consequently the row total doubles with each successive row. If the row containing a single '1' is row zero, then T = 2r where T is the sum of the numbers in row r. So for r=100 T = 2100 = 1267650600228229401496703205376

the horizontal sums doubles each time the sum of row 1 = 1 row 2= 2 row 3 = 4 row 4 = 8 row 5 = 16 etc etc.......... the horizontal sums doubles each time the sum of row 1 = 1 row 2= 2 row 3 = 4 row 4 = 8 row 5 = 16 etc etc..........

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.

Related questions

16020

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

Sum of numbers in a nth row can be determined using the formula 2^n. For the 100th row, the sum of numbers is found to be 2^100=1.2676506x10^30.

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.)

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

64

8000 Numbers are: 381 383 385 387 389 391 393 395 397 399 401 403 405 407 409 411 413 415 417 419

=SUM(A1:A17) for example

Each number in Pascal's triangle is used twice when calculating the row below. Consequently the row total doubles with each successive row. If the row containing a single '1' is row zero, then T = 2r where T is the sum of the numbers in row r. So for r=100 T = 2100 = 1267650600228229401496703205376

18 + 19 + 20 = 57

the horizontal sums doubles each time the sum of row 1 = 1 row 2= 2 row 3 = 4 row 4 = 8 row 5 = 16 etc etc.......... the horizontal sums doubles each time the sum of row 1 = 1 row 2= 2 row 3 = 4 row 4 = 8 row 5 = 16 etc etc..........

You use the sum function whenever you wish to total up a column or row of numbers.

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