Sequences and Series — Formula Sheet

a_n = 2n

a_n = (n - 1)(2 - n)(3 + n)

a_n = 4n - 3

a_n = n^2 / 2^n

a_1 + a_2 + a_3 + ... + a_n = Σ_{k=1}^n a_k

S_n

a_n = ar^{n-1}

S_n = na

S_n = a(r^n - 1)/(r - 1) = a(1 - r^n)/(1 - r)

r = a_{k+1}/a_k

The expression a1 + a2 + a3 + ... + an is written as sum from k=1 to n of ak.

If r = 1, then all terms are equal and S_n = na.