$\sum_{n=1}^{\infty}\frac{(-2)^n}{\sqrt n}{(x+7)^n}$
What did I do wrong?
I used the ratio test and got:
2|x+7| < 1
And for my radius I got $\frac {1}{2}$
After, I solved the inequality and got the interval [-15/2,-13/2]
But webwork is telling me I'm incorrect. I also tried to see if (-15/2,-13/2) would work but it did not.
UPDATE: As the comments suggested I tested the endpoints and the correct interval is:
(-15/2, -13/2]
To test the end points,
When $x = \frac{-13}2$, the series becomes
$$\sum_{n=1}^\infty \frac{(-1)^n}{\sqrt{n}},$$
since $\frac1{\sqrt{n}}$ decreases to $0$, by alternativing series test, the series converges.
When $x=\frac{-15}2$, the series becomes $$\sum_{n=1}^\infty \frac{1}{\sqrt{n}},$$ and by $p$-series test, it diverges.