{"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 $\\dfrac{2}{1},\\dfrac{3}{2},\\dfrac{5}{3},\\dfrac{8}{5},\\dfrac{13}{8},\\dfrac{21}{13}$。求这个分数序列的前 $n$ 项之和。\n\n## Input\n\n输入一行一个正整数 $n(n\\leq 30)$。\n\n## Output\n\n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。\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"LGB2069","tags":["循环结构"],"sample_group":[["2","3.5000"]],"created_at":"2026-03-03 11:09:25"}}