Question #ab36d

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Answer 1 · 2017-09-26T10:41:30

$-5 < x < -1$

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

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 $-5 < x < -1$ .