very difficult math question?

[chuismile]

Find an infinite geometric series that represents the given function, and state the interval of convergence

Y= 2/1-3x

[gillespiebkk]

The answer is 23. Or Belgium.

[Jessica J]

You can use the identity of y = 1 / (1-x) which is the summation of x^n from n = 0 to infinity. Simply plugin the new values for x (which is 3x) and then multiply the identity by two to find the series for the equation. It would be

? 2(3x)^n from n = 0 to infinity.
2 [ 1 + 3x + 9x^2 + 27x^3 + .... 3^n * x^n ]

The interval of convergence for the identity is (-1, 1). If we plugin our new value of x we'd get
-1 < 3x < 1
Which leaves us with
-1/3 < x < 1/3

So the interval of convergence is (-1/3, 1/3) and the series that represents the function is ? 2(3x)^n from n = 0 to infinity.