FORMULARIO POLINOMIOS DE MACLAURIN

POLINOMIOS DE MACLAURIN: FORMULARIO

x2 x3 xn
ex 1+x+ + +. . . +
2! 3! n!


x3 x5 x 2n+1
𝑠𝑒𝑛 𝑥 x- + - . . . +ሺ-1ሻn
3! 5! ሺ2n + 1ሻ!



x2 x4 x 2n
𝑐𝑜𝑠 𝑥 1- + - . . . +ሺ-1ሻn
2! 4! ሺ2nሻ!



x3 x5 x 2n+1
𝑠𝑒𝑛ℎ 𝑥 x + + +...+
3! 5! ሺ2n + 1ሻ!



x2 x4 x 2n
𝑐𝑜𝑠ℎ 𝑥 1 + + - . . . +ሺ-1ሻn
2! 4! ሺ2nሻ!



x2 x4 xn
𝑙𝑜𝑔 ሺ1 + 𝑥 ሻ 1 + + - . . . +ሺ-1ሻn-1
2! 4! n


α α α α
ሺ1 + xሻα 1 + ( ) x + ( ) x 2 + ( ) x 3 +. . . + ( ) x n
1 2 3 n


x3 x5 x 2n+1
𝑎𝑟𝑐 𝑡𝑎𝑛 𝑥 x- + - . . . +ሺ-1ሻn
3 5 2n + 1


1 x3 1 · 3 x5 1 · 3 · 5 x7 1 · 3 ··· ሺ2n-1ሻ x 2n+1
arc sen x x + · + · + · +...+ ·
2 3 2·4 5 2·4·6 7 2 · 4 ··· ሺ2nሻ 2n + 1




Recordemos que si α ∈ ℝ y k ∈ ℕ, se define
α α αሺα-1ሻ ··· ሺα-k + 1ሻ
( ) = 1, ( )=
0 k k!