六题求解

surftan

六题求解

magicstrawberry

目测不是特别困难，除了5可能有美丽的解法外，其他不好说

282842712474

这类题目其实大部分都可以交给AI了：

点击链接查看和 Kimi 的对话 https://www.kimi.com/share/19d85559-44d2-86af-8000-000075fa62da

surftan

都是基础的题哈，没方法没思路不行。

王守恩

第5题。来个更强的。n=1,2,3,4,5,6,...。证明: \(\D\big\lfloor\sqrt{n}+\sqrt{n+1}+\sqrt{n+2}\ \big\rfloor=\big\lfloor\sqrt{9n+7}\ \big\rfloor\)

因为。\(\D\big\lfloor\sqrt{n}+\sqrt{n+1}+\sqrt{n+2}\ \big\rfloor>\big\lfloor\sqrt{9n+8}\ \big\rfloor>\big\lfloor\sqrt{9n+7}\ \big\rfloor\)

扩大。

\(\D\big\lfloor\sqrt{n}\ \big\rfloor=\big\lfloor\sqrt{n+0}\ \big\rfloor\)

\(\D\big\lfloor\sqrt{n}+\sqrt{n+1}\ \big\rfloor=\big\lfloor\sqrt{4n+1}\ \big\rfloor\)

\(\D\big\lfloor\sqrt{n}+\sqrt{n+1}+\sqrt{n+2}\ \big\rfloor=\big\lfloor\sqrt{9n+7}\ \big\rfloor\)

\(\D\big\lfloor\sqrt{n}+\sqrt{n+1}+\sqrt{n+2}+\sqrt{n+3}\ \big\rfloor=\big\lfloor\sqrt{16n+20}\ \big\rfloor\)

\(\D\big\lfloor\sqrt{n}+\sqrt{n+1}+\sqrt{n+2}+\sqrt{n+3}+\sqrt{n+4}\ \big\rfloor=\big\lfloor\sqrt{25n+49}\ \big\rfloor\)

\(\D\big\lfloor\sqrt{n}+\sqrt{n+1}+\sqrt{n+2}+\sqrt{n+3}+\sqrt{n+4}+\sqrt{n+5}\ \big\rfloor=\big\lfloor\sqrt{36n+88}\ \big\rfloor\)

得到一串数(找最小的)——{0,1,7,20,49,88,144,217,322,449,603,784,1013,1269,1566,1913,2311,2752,3247,3796,4405,5080,5814,6601,7499,8449,9475,10564,11773,13041,14412,15865,17422,
19073,20819,22672,24641,26712,28890,31184,33619,36157,38827,41617,44539,47605,50802,54121,57621,61249,65023,68948,73033,77272,81669,86209,90970,95873,100947,106164}——OEIS没有。

这串数肯定有问题——坐等高手。