Simple question about Sinc()
No, the signal 
$$
h[n] = \frac{\sin(\omega_c \, n)}{\pi \, n}, \qquad -\infty &lt; n &lt; \infty
$$

is not absolutely summable, as the sum

$$
\sum_{n=-\infty}^{\infty} \Big|h[n]\Big| = \sum_{n=-\infty}^{\infty} \left |\frac{\sin(\omega_c \, n)}{\pi \, n} \right| 
$$

diverges to infinity. Hence the absolute sum does not converge and therefore it's considered as an unstable system's impulse response. Yet, its square is absolutely summable:

$$
\sum_{n=-\infty}^{\infty} \Big|h[n]\Big|^2 = \sum_{n=-\infty}^{\infty} \left |\frac{\sin(\omega_c \, n)}{\pi \, n} \right|^2 
$$
does not diverge. This kind of condition is stated as mean square convergence; i.e., a typical condition for discontinuous frequency responses that has finite jumps in its frequency response which should be continuous for all $\omega$ according to the Fourier theorem that would require uniform convergence at all frequency points $\omega$.