The range of n-bit signed magnitude representation is

For an $n$-bit Signed Magnitude Representation:
The leftmost bit (MSB) is the sign bit:
$0 \rightarrow$ Positive
$1 \rightarrow$ Negative
Remaining $(n-1)$ bits represent the magnitude
Maximum positive value:
Sign bit $= 0$, remaining $(n-1)$ bits all $1$s
$\Rightarrow +(2^{n-1} - 1)$
Maximum negative value:
Sign bit $= 1$, remaining $(n-1)$ bits all $1$s
$\Rightarrow -(2^{n-1} - 1)$
Note: $+0$ and $-0$ both exist in signed magnitude representation
$\therefore$ Range of $n$-bit Signed Magnitude Representation is:
$\therefore \boxed{-(2^{n-1}-1) \leq x \leq +(2^{n-1}-1)}$