Series

Serie Aritmética:

$S_arit = {(t_1 + t_n).n}/2$

donde:

$S_geom = { t_1 (q^n - 1) }/{ q - 1 }$

donde:

$S_infin = t_1 / {1 - q}$

donde:

1+2+3+ ... n ~=~ {n(n + 1)}/2

$n^2 ~=~ { n (n + 1)(2n + 1) }/6$

$(2n)^2 ~=~ { 2n (2n + 1)(2n + 2) }/6 ~=~ { 2n (n + 1)(2n + 1) }/3$

$(2n -1)^2 ~=~ { (2n - 1)(2n)(2n + 1) }/6 ~=~ { n ( 4n^2 - 1 ) }/3$

$n^3 ~=~ ( { n(n+1) }/2 )^2$

(2n)^3 ~=~ 2( n(n+1) )^2

(2n -1)^3 ~=~ n^2 (2n^2 -1)

n(n+1) ~=~ {n(n+1)(n+2)}/3

n(n+1)(n+2) ~=~ {n(n+1)(n+2)(n+3)}/4

1/{n.(n + 1)} ~=~ n/(n+1)