To expand on what has already been said...
Code:
cat null_math
#!/bin/bash
unset a
echo $((a+1))
echo $((1+a))
echo $(($a+1))
echo $((1+$a))
./null_math
1
1
1
./null_math: line 8: 1+: syntax error: operand expected (error token is "+")
You will see that only the last case fails.
The first one evaluates to 0+1 per the pasted man page snippet.
The second one evaluates to 1+0, again per the man page.
The third, which uses parameter expansion, evaluates to +1 which is just the value, +1.
The fourth, also using parameter expansion, fails because it evaluates to 1+ (nothing after the +), hence the message about the missing operand.