Sequences and Series

Arithmetic Sequence

[Ex: 2,4,6,8,10] an = a1 + d(n - 1) a1: first term (2) d: common difference (2) nth term: an = 2 + 2(n - 1) => an = 2 + 2n - 2 => an = 2n

Geometric Sequence

[Ex: 2,4,8,16,32] an = a1(r)**n-1 a1: first term (2) r: common ratio (2) nth term: a1(r)**n-1

Convergent Series

a sequence who's partial sums tend to a limit; that means that the partial sums become closer and closer to a given number when the number of their terms increases.

Divergent Series

an infinite series that is not convergent, meaning that the infinite sequence of the partial sums of the series does not have a finite limit.

Term below the sigma

First Term

Expression in front (right) of the sigma

Formula meant to find the sum of a series.

Arithmetic Series

Formula to find the nth partial sum of a () series Sn = n/2(a1 + an) an: last term [Ex: 2,4,6,8,10] S5 = 5/2(2+10) S5 = 2.5(12) S5 = 30

Geometric Series

Formula to find the sum of a () series Sn = a1(1 - r**n/1 - r) [Ex: 2,4,8,16,32] S5 = 2(1 - 2**5/1 - 2) S5 = 2(1 - 32/-1) S5 = 2(- 31/-1) S5 = 2(31) S5 = 62

Term on above the sigma

Last Term