The expansion of F (x) = 1 / (2 + x) into a power series of X It also points out the establishment range

The expansion of F (x) = 1 / (2 + x) into a power series of X It also points out the establishment range

F (x) = 1 / (2 + x) = 1 / 2 * 1 / (1 + X / 2) = 1 / 2 ∑ (n from 0 to ∞) (- X / 2) ^ n = ∑ (n from 0 to ∞) (- 1) ^ n / (2 ^ (n + 1)) x ^ n
|x/2|