算术运算为什么加$

1 #!/bin/bash
2 # Program:
3 # Try do calculate 1+2+...+${you_input}
4 # History:
5 # 2015/07/17 VBird First release
6 PATH=/bin:/sbin:/usr/bin:/usr/sbin:/usr/local/bin:/usr/local/sbin:~/bin
7 export PATH
8
9 read -p "Please input a number,I will count for 1+2+...+your_input:" nu
10
11 s=0
12 for ((i=1; i<=${nu}; i=i+1))
13 do
14 s=$((${s}+${i}))
15 done
16 echo "The result of '1+2+3+...+${nu}' is ==> ${s}"

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为什么 14 行中的赋值算术运算需要在大括号前加$，不加就报错