competition math formulas

Permutations forumala - choosing items from a set where order does not matter

n!/(n-r)!

number of factors formula

Add 1 to each exponent of the prime factorization

72 = 2³ * 3²

(3+1)*(2+1) = 4×3 = 12 factors

Total number of rectangles of any size of a m*n grid

(m(m+1))/2 * (n(n+1))/2

Finding a term of a arithmetic sequence

𝑎𝑛=𝑎1+(𝑛−1)𝑑

Sum of N terms

n((first term + last term)/2) where n = number of terms

Sum of consecutive numbers till N

(N(N+1))/2

Sum of factors formula

ex. sum of factors of 90

90 = 2^1 × 3² * 5^1

(2^0 + 2^1) * (3^0 + 3^1 + 3²) (5^0 + 5^1)

(1+2) * (3+1+9) * (1+5)

3×13×6

234

finding a term of a geometric sequence formula

Sum of terms for geometric sequences