  We compute exactly the mean number of records $\langle R_N \rangle$ for a
time-series of size $N$ whose entries represent the positions of a discrete
time random walker on the line. At each time step, the walker jumps by a length
$\eta$ drawn independently from a symmetric and continuous distribution
$f(\eta)$ with probability $1-r$ (with $0\leq r < 1$) and with the
complementary probability $r$ it resets to its starting point $x=0$. This is an
exactly solvable example of a weakly correlated time-series that interpolates
between a strongly correlated random walk series (for $r=0$) and an
uncorrelated time-series (for $(1-r) \ll 1$). Remarkably, we found that for
every fixed $r \in [0,1[$ and any $N$, the mean number of records $\langle R_N
\rangle$ is completely universal, i.e., independent of the jump distribution
$f(\eta)$. In particular, for large $N$, we show that $\langle R_N \rangle$
grows very slowly with increasing $N$ as $\langle R_N \rangle \approx
(1/\sqrt{r})\, \ln N$ for $0<r <1$. We also computed the exact universal
crossover scaling functions for $\langle R_N \rangle$ in the two limits $r \to
0$ and $r \to 1$. Our analytical predictions are in excellent agreement with
numerical simulations.
