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What is the sum of all the numbers in a pascal triangle with 50 rows?
Wiki User
∙ 14y ago
The first row of Pascal's triangle is 1,1 with a sum of 2
The second row is 1,2,1 with a sum = 4 = 22
The third row is 1,3,3,1 with a sum = 8 = 23
The nth row sums to 2n
Suppose S = 2+22+...+250
then 2*S = 22+23+...+251
Subtracting the first from the second,
S = 251 - 2 which, if my calculator serves me right, is
2,251,799,813,685,246
Wiki User
∙ 14y ago
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What is the sum of all the numbers in row 50 of Pascal's triangle?
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.)
What is the History of Pascal's triangle?
The set of numbers that form Pascal's triangle were well known before Pascal. But, Pascal developed many applications of it and was the first one to organize all the information together in his Traité du triangle arithmétique (1653). The numbers originally arose from Hindu studies of binomial numbers and the study of figurate numbers. The earliest explicit depictions of a triangle of binomial coefficients occur in the 10th century in commentaries on the Chandas Shastra, a book by Pingala written between the 5th and 2nd century BC.
What does triangular number mean?
Triangluar numbers or triangle numbers are numbers formed from the summation of all the numbers smaller than them. The first few triangle numbers are 1,3,6,10,15,21... If you think of a pyramid with a base of two blocks, and one on top, there are three blocks. If you add a base of three to that pyramid, you have six blocks. Then ten, and fifteen and so on. That is why they are called Triangle numbers.
Name all the factor pairs of 12 showing each one using an array?
1 row of 12 12 rows of 1 3 rows of 4 4 rows of 3 2 rows of 6 6 rows of 2
If you have 24 juice cans show all of the ways you can arrange these cans into arrays?
There are eight possible combinations... 1 row of 24 cans 2 rows of 12 cans 3 rows 8 cans 4 rows of 6 cans 6 rows of 4 cans 8 rows of 3 cans 12 rows of 2 cans 24 rows of 1 can
What is the sum of all the numbers in row 50 of Pascal's triangle?
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.)
What are the patterns in a pascal's triangle?
Pascal's rule for his triangle pattern is all the sides are ones
What is the History of Pascal's triangle?
The set of numbers that form Pascal's triangle were well known before Pascal. But, Pascal developed many applications of it and was the first one to organize all the information together in his Traité du triangle arithmétique (1653). The numbers originally arose from Hindu studies of binomial numbers and the study of figurate numbers. The earliest explicit depictions of a triangle of binomial coefficients occur in the 10th century in commentaries on the Chandas Shastra, a book by Pingala written between the 5th and 2nd century BC.
What did pascal do for maths?
he invented the pascal triangle . it is a triangle where every two numbers add up to the number below them while there are all 1's going all the way down each diagonal side of the triangle. he also invented the first mechanical calculator machine.
What kind of numbers do we find in pascal's triangle?
All counting numbers. In fact the second number in each row forms the sequence 1,2,3,4,...
Things invented by Blaise Pascal?
The Pascal's triangle was named after Blaise Pascal the creator of this triangle. Blaise pascal was born June 19, in Claremont He was a famous French mathematician and philosopher. Pascal's triangle was developed by the Chinese, but it was Blaise who discovered the importance of all the patterns it contained. At the age of 18 he invented a numerical wheel calculator called the pascaline, which about 8 years later he further improved. He then died in 1662, from a sickness he had since he was seventeen called insomnia and acute dyspepsiaicate, caused by incessant study. hope that helps :)
How does Pascals triangle work?
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 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). In this way, the rows of the triangle go on infinitly. A number in the triangle can also 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)!].
What is a pascal's triangle used for?
It is used for lots of things such as finding out the total possible outcomes of tossing coins. You find the line that corresponds with how many coins you toss and add all the numbers in that line to get the number of possible outcomes also you can use it to find combinations and permutations and triangular numbers
How to get an answer for a pascal triangle?
I placed a link to a page that tells you all about it! If you need more specific information just ask here at Answers.com
What is the triangle number out of all the prime numbers?
3
Can sums all rows equal 9 using 0 - 8 only once?
There are 9 numbers. Assuming the question refers to a 3x3 "magic" square, the answer is no. The sum of all nine numbers is 36 so each of the 3 rows must sum to 12.
How do you find the ratio of the volume of a cube?
you multiply all numbers you see. If triangle you multiply all numbers then divide it by three
