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What is Pascal's triangle?
Blaise Pascal published the workings of a triangular array showing the relationship between binary coefficients in said triangle. For instance:__________________________________________|.......................................1.........................................||..................................1........1....................................||..............................1.......2........1...............................||..........................1......3........3.......1...........................||......................1......4.......6.......4......1........................||...................1......5.....10....10......5......1...................||...............1......6.....15....20.....15.....6.....1...............||_________________________________________|Each number in the above triangle is the sum of the two numbers right about it.For example, 20 is the sum of 10 and 10, and 2 is the sum of 1 and 1.
What is the sum of 645 and 10?
Sum means adding so the sum is 645 + 10 = 655. Hope it helped!
What is the sum of the first 10 multiples of 3?
The sum of the first 10 multiples of 3 is 165.
What is 6125 in expanded form as an addition expression?
6000 + 100 + 20 + 5
What must be added to the binomial m2-12m to make it a perfect square trinomial?
-10
What is the coefficients 15b plus 23b plus 10?
In the expression '15b + 23b + 10', the coefficients are 15, 23, and 10.If you simplify the expression to '38b + 10", then the coefficients are 38 and 10.
Pascal's triangle how it it used in binomial expansion?
You can find the coefficients of an expanded binomial using the numbers in Pascal's triangle. 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 1 6 15 20 15 6 1 1 7 21 35 35 21 7 1 These are a few rows of Pascals triangle. Now let's look at a few binomials, expanded to the second and third powers. (a+b)2=a2 +2(ab) + b2 notice the coefficients are the numbers in the second row of the triangle above. (a+b)3= a3+3(a2b)+3(ab2)+b3 and once again note that the coefficients are the numberin the third line of Pascal's triangle. The first line, by the way, which is 1,1 is the coefficient of (a+b)1 This will work for any power of the binomial. There are generalized form for non-integer powers.
What is the sum of 4 over10 expressed in simplest form?
4/10 = 2/5 as a fraction in its simplest form
What is the sum of 10 plus 10?
the sum of 10 + 10 = 20
What has the sum of 57 over 100?
37/100+2/10
What is a sum of 10?
A sum is the addition of any numbers to produce another number. In your case, you have to find any numbers that will add up to 10. The sum of 10 and 0 is 10, the sum of 5 and 5 is 10, the sum of 2 and 8 is 10, the sum of -2 and 12 is 10, so there are an infinite amount of answers for your question.
What is the sum of the first multiple of 10?
The sum of 10*1 is 10.
How is Pascal's triangle related to the Binomial Theorem?
I think an example will help most people see it better than just an explanation/answer. So first a few examples are presented and than a general answer.Start with (1+x)2 = 1+2x+x2 and look at the coefficients of the results you will see that they are 1, 2, 1. Now do it for (1+x)3 and they are 1, 3, 3, 1. These, of course, are the lines from Pascal's Triangle. I put the first part of the triangle below (in left-justified form). You should notice that when the exponent is 2, we use the third line and when the exponent is 3, we use the fourth line of the triangle.11 11 2 11 3 3 11 4 6 4 11 5 10 10 5 11 6 15 20 15 6 11 7 21 35 35 21 7 11 8 28 56 70 56 28 8 11 9 36 84 126 126 84 36 9 1In case you wonder about the first two rows. Look at (1+x)0 and(1+x)1, their coefficients come from those two rows.Now look at (a + b)4 = a4 + 4a3b + 6a2b2 + 4ab3 + b4 which is more general and of course the coefficients come from the 5th line of the triangle.So the answer to the question is that if we look at the binomial (a + b)nThe n+1 row of Pascal's triangle gives us the coefficients of the expanded form of the binomial. Seeing the examples first often makes this easier to see and understand. It is the n+1 row because the first row of the triangle is any binomial with an exponent of 0.
What is the sum of x and 10?
the sum equals x+10
What is Pascal's triangle?
Blaise Pascal published the workings of a triangular array showing the relationship between binary coefficients in said triangle. For instance:__________________________________________|.......................................1.........................................||..................................1........1....................................||..............................1.......2........1...............................||..........................1......3........3.......1...........................||......................1......4.......6.......4......1........................||...................1......5.....10....10......5......1...................||...............1......6.....15....20.....15.....6.....1...............||_________________________________________|Each number in the above triangle is the sum of the two numbers right about it.For example, 20 is the sum of 10 and 10, and 2 is the sum of 1 and 1.
What is the sum of 2 and 8?
The sum of 8 and 2 is 10
What is the sum 10?
10.
