Pascals Triangle

Front

What is Pascal's Triangle?

Back

A triangular array of the binomial coefficients, where each number is the sum of the two directly above it.

Front

What is the formula to find the nth row of Pascal's Triangle?

Back

The nth row corresponds to the coefficients of the expansion of (a + b)^n.

Front

What are the coefficients of the 6th row in Pascal's Triangle?

Back

1, 6, 15, 20, 15, 6, 1.

Front

How do you expand (x + 3)^6 using Pascal's Triangle?

Back

Use the coefficients from the 6th row: 1, 6, 15, 20, 15, 6, 1 to expand.

Front

What is the sum of the numbers in the nth row of Pascal's Triangle?

Back

2^n.

Front

What is the relationship between Pascal's Triangle and combinations?

Back

The entries in Pascal's Triangle represent the binomial coefficients, which are combinations of n items taken k at a time.

Front

What is the 5th row of Pascal's Triangle?

Back

1, 5, 10, 10, 5, 1.

Front

How many rows does Pascal's Triangle have?

Back

Infinite.

Front

What is the significance of the diagonal in Pascal's Triangle?

Back

The diagonals represent the triangular numbers, which count objects arranged in an equilateral triangle.

Front

What is the 4th row of Pascal's Triangle?

Back

1, 4, 6, 4, 1.