#### Answer

The series $\sum_{n=1}^{\infty} \frac{(-1)^{n} }{ 1+(1/n)}$ diverges.

#### Work Step by Step

We have the absolute series
$$\sum_{n=1}^{\infty} |\frac{(-1)^{n} }{ 1+(1/n)}|=\sum_{n=1}^{\infty} \frac{1}{ 1+(1/n)}.$$
So, we have $$\lim_{n\to \infty }b_n=\lim_{n\to \infty } \frac{1}{ 1+(1/n)}=\lim_{n\to \infty } \frac{1 }{ 1+0}=1\neq 0.$$
Thus the positive series diverges by the divergence test.
We see that the terms $\frac{1}{ 1+(1/n)}$ are not decreasing.
Thus the original series $\sum_{n=1}^{\infty} \frac{(-1)^{n} }{ 1+(1/n)}$ does not converge absolutely or conditionally.