Adding and Counting

Question 1

the number of ordered arrangements of n distinct things

Answer 1

n!

Question 2

Sum of a Geometric Sequence

Answer 2

1+r^1+r^2+r^3+…r^n=((r^n+1)-1)/r-1

Question 3

Sum of an Arithmetic Sequence

Answer 3

is the average of the first and last terms, multiplied by the
number of terms (the number of terms is one more than the difference between the first and last
terms divided by the common difference)

Question 4

the number of ways to choose k things from a set of n things if duplicates are allowed

Answer 4

(n+k-1)!/k!(n-1)

Question 5

Gauss’s Formula

Answer 5

1+2+3+…+n=(n(n+1)/2

Question 6

the number of ways to choose a set of k distinct things from a set of n distinct things (“n
choose k”)

Answer 6

nCk=n!/(n-k)!k!

Question 7

Difference of two squares

Answer 7

x^2-y^2=(x-y)(x+y)