Write an equivalent series with the index of summation beginning at n = 1. ∞ (−1)n + 1(n + 1)xn n = 0

Looks like the starting series is

Note the degree of the first few terms in the series, for , are , and so on.

So if the series were to start at , we would need to preserve that pattern, and we do that by replacing with :

Simplifying a bit, we end up with

x=-2

infinite number of lines, so there is an infinite number of equations.

step-by-step explanation:

there are an infinite number of line that passes through the point (-2,5)

x=-2   is one line that passes through the point

y = 5 is another line that passes through the point

(these two lines are perpendicular to each other).

since the number of   numbers are infinite and the slope is the ratio of two numbers,(change in y over change in x) we can have an infinite number of slopes.     our only condition is that it passes through the point (-2,5)