math formulas

series and sequences im ending it

explicit formula for arithmetic sequence

a_n = a_n-1 · d

recursive formula for arithmetic sequence

a_n = a_n-1 + d

t_n+1 = t_n + d ; t₁ = #

What formula always requires the label of T₁ before any solving?

RECURSIVE FORMULAS! Both arithmetic AND geometric!

Geomtric explicit formula

a_n = a₁ · r^n-1

Geomtric recursive formula

a_n = a_n-1 · r

Partial sum of an arithmetic series

S_n = n/2 (2 t₁ + (n-1)d)

Partial sum of a geometric series

S_n = a1 · (1 - rⁿ) / (1 - r) for r ≠ 1

Where S_n, a geometric series, converges to

S = a₁ / (1 - r) for |r| < 1

what does |r| < 1 do?

converge

what does |r| >1 do?

DIverge

The binomial formula

What is (n / k)

n! / (k! (n - k)!)