Alpha algebra

What are the coefficients in the 3rd row / 2nd power of pascal’s triangle?

1 ; 2 ; 1

What are the coefficients in the 4th row / 3rd power of pascal’s triangle?

1 ; 3 ; 3 ; 1

What are the coefficients in the 5th row / 4th power of pascal’s triangle?

1 ; 4 ; 6 ; 4 ; 1

What are the coefficients in the 6th row / 5th power of pascal’s triangle?

1 ; 5 ; 10 ; 10 ; 5 ; 1

What are the coefficients in the 7th row / 6th power of pascal’s triangle?

1 ; 6 ; 15 ; 20 ; 15 ; 6 ; 1

Formula for a binomial expansion using pascals triangle

(a + b)ⁿ = aⁿb⁰ + Ca^n-1b¹ + Ca^n-2b² … Ca¹b^n-1 + a⁰bⁿ where C is the coefficient determined by pascal’s triangle

What is the formula of the binomial theorem (Not simplified)

Binomial theorem simplified with combinations

How to find the nth term with binomial theorem

Where:
r is the term number you want
n is the power binomial
a the first term in the binomial
b is the second term in the binomial

Steps for rieman sum (Notes)