  For the one-dimensional long-ranged Ising spin-glass with random couplings
decaying with the distance $r$ as $J(r) \sim r^{-\sigma}$ and distributed with
the L\'evy symmetric stable distribution of index $1 <\mu \leq 2$ (including
the usual Gaussian case $\mu=2$), we consider the region $\sigma>1/\mu$ where
the energy is extensive. We study two real space renormalization procedures at
zero temperature, namely a simple box decimation that leads to explicit
calculations, and a strong disorder decimation that can be studied numerically
on large sizes. The droplet exponent governing the scaling of the renormalized
couplings $J_L \propto L^{\theta_{\mu}(\sigma)}$ is found to be
$\theta_{\mu}(\sigma)=\frac{2}{\mu}-\sigma$ whenever the long-ranged couplings
are relevant $\theta_{\mu}(\sigma)=\frac{2}{\mu}-\sigma \geq -1$. For the
statistics of the ground state energy $E_L^{GS}$ over disordered samples, we
obtain that the droplet exponent $\theta_{\mu}(\sigma) $ governs the leading
correction to extensivity of the averaged value $\overline{E_L^{GS}} \simeq L
e_0 +L^{\theta_{\mu}(\sigma)} e_1$. The characteristic scale of the
fluctuations around this average is of order $L^{\frac{1}{\mu}}$, and the
rescaled variable $u=(E_L^{GS}-\overline{E_L^{GS}})/L^{\frac{1}{\mu}}$ is
Gaussian distributed for $\mu=2$, or displays the negative power-law tail in
$1/(-u)^{1+\mu}$ for $u \to -\infty$ in the L\'evy case $1<\mu<2$.
