The power seris (in one variable) is an infinite series of the form. where an represents the coefficient of the nth term, c is a constant, and x varies around c (for this reason one sometimes speaks of the series as being centered at c).

A seris \(f(x) = \sum_{n=0}^\infty a_n \left( x-c \right)^n = a_0 + a_1 (x-c)^1\) Note that i only put the first variable here, but like i said it tends to infinity THE ANSWEAR IS not \( a_0 + a_1 (x-c)^1\)