Question

Question #ab36d

Answer 1

`-5 < x < -1`

Explanation:

`((x + 3)^(n-1))/(2^n) = ((x + 3)^n)/((x+3)*2^n) = 1/(x+3) ((x+3)/2)^n`

Then we get that `sum ((x+3)/2)^n` converges when `|\ (x+3)/2 | < 1`.

So we solve for `x`

`-1 < (x+3)/2 < 1`

`-2 < x+3 < 2`

`-5 < x < -1`

Then we have that `1/(x+3)` is just a constant, and so we get that

`1/(x+3) sum ((x+3)/2)^n` converges when `-5 < x < -1`.