Which of the following statements regarding Pascal's triangle are correct?

AEach row is a \"palindrome\" — that is, it is the same if read from left to right or from right to left.
BThe coefficients of (x + y)n are given by the nth row of Pascal's triangle.
CTo generate Pascal's triangle, add adjacent terms on a row to determine the term directly below them.
DThe nth row gives the coefficients in the expansion of (x + y) n-1.

Question

roCanlaffyle roCanlaffyle

29-07-2016
Mathematics

Answered

Which of the following statements regarding Pascal's triangle are correct?

AEach row is a \"palindrome\" — that is, it is the same if read from left to right or from right to left.
BThe coefficients of (x + y)n are given by the nth row of Pascal's triangle.
CTo generate Pascal's triangle, add adjacent terms on a row to determine the term directly below them.
DThe nth row gives the coefficients in the expansion of (x + y) n-1.

Verified Answer :

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flightbath flightbath · Answer 1 · 2019-01-03T04:12:28-05:00

Answer:

Option A, C and D are correct.

Step-by-step explanation:

Option A is correct because if we take example of \((x+y)^3\) we get:

1,2,1

1,3,3,1

1,4,6,4,1

So we can see that either we read left to right or right to left we are getting same row

Option B is not correct because When we take power zero it will occupy first row hence, \((x+y)^n\) is not given by nth row.

Option C is correct because adding adjacent terms on a will give us the term directly below look at the example in option A.

Option D is correct because nth row will give coefficients in the expansion of (x + y) n-1 since, zero will occupy first row hence, nth row will be n-1.

maheshpatelvVT maheshpatelvVT · Answer 2 · 2022-08-05T08:43:03-04:00

Statement (A), statement (B), and statement (C) are correct as the binomial coefficients are geometrically represented as a triangle by Pascal's triangle in mathematics.

What is the triangle?

In terms of geometry, the triangle is a three-sided polygon with three edges and three vertices. The triangle's interior angles add up to 180°.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

The binomial coefficients are geometrically represented as a triangle by Pascal's triangle in mathematics.

Slightly more simply, the value of each element is the sum of the items to its left and right, and each row is one element longer than the row before it (if these exist).

This results in one at the start and end of each row. Both the row and column counts begin at one.

Thus, statement (A), statement (B), and statement (C) are correct as the binomial coefficients are geometrically represented as a triangle by Pascal's triangle in mathematics.

Learn more about the triangle here:

brainly.com/question/25813512

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