求分数序列和

Luogu

IDLGB2069

Time1000ms

Memory128MB

DifficultyP1

循环结构

有一个分数序列 $\dfrac{q_{1}}{p_{1}},\dfrac{q_{2}}{p_{2}},\dfrac{q_{3}}{p_{3}},\dfrac{q_{4}}{p_{4}},\dfrac{q_{5}}{p_{5}},...$，其中 $q_{i+1}=q_{i}+p_{i}, p_{i+1}=q_{i},p_{1}=1,q_{1}=2$。比如这个序列前 $6$ 项分别是 $\dfrac{2}{1},\dfrac{3}{2},\dfrac{5}{3},\dfrac{8}{5},\dfrac{13}{8},\dfrac{21}{13}$。求这个分数序列的前 $n$ 项之和。 ## Input 输入一行一个正整数 $n(n\leq 30)$。 ## Output 输出一行一个浮点数，表示分数序列前 $n$ 项的和，精确到小数点后 $4$ 位。 [samples]

Samples

Input #1

Output #1

3.5000

API Response (JSON)

{
  "problem": {
    "name": "求分数序列和",
    "description": {
      "content": "有一个分数序列 $\\dfrac{q_{1}}{p_{1}},\\dfrac{q_{2}}{p_{2}},\\dfrac{q_{3}}{p_{3}},\\dfrac{q_{4}}{p_{4}},\\dfrac{q_{5}}{p_{5}},...$，其中 $q_{i+1}=q_{i}+p_{i}, p_{i+1}=q_{i},p_{1}=1,q_{1}=2$。比如这个序列前  $6$ 项分别是 $\\dfrac",
      "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": "LGB2069"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "有一个分数序列 $\\dfrac{q_{1}}{p_{1}},\\dfrac{q_{2}}{p_{2}},\\dfrac{q_{3}}{p_{3}},\\dfrac{q_{4}}{p_{4}},\\dfrac{q_{5}}{p_{5}},...$，其中 $q_{i+1}=q_{i}+p_{i}, p_{i+1}=q_{i},p_{1}=1,q_{1}=2$。比如这个序列前  $6$ 项分别是 $\\dfrac...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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