计算分数加减表达式的值

{
  "problem": {
    "name": "计算分数加减表达式的值",
    "description": {
      "content": "$S_n=\\frac{1}{1}-\\frac{1}{2}+\\frac{1}{3}-\\frac{1}{4}+\\frac{1}{5}-\\frac{1}{6}+...+(-1)^{n-1}\\times\\frac{1}{n}$。 输入一个整数 $n$，求 $S_n$。",
      "description_type": "Markdown"
    },
    "platform": "Luogu",
    "limit": {
      "time_limit": 1000,
      "memory_limit": 131072
    },
    "difficulty": {
      "LuoguStyle": "P1"
    },
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "LGB2070"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "$S_n=\\frac{1}{1}-\\frac{1}{2}+\\frac{1}{3}-\\frac{1}{4}+\\frac{1}{5}-\\frac{1}{6}+...+(-1)^{n-1}\\times\\frac{1}{n}$。\n\n输入一个整数 $n$，求 $S_n$。\n\n## Input\n\n输入为一行，含一个正整数 $n$。\n\n## Output\n\n输出为一行，为 $S_n$ 的值，结果保留小数点后 $...",
      "is_translate": false,
      "language": "English"
    }
  ]
}