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徐森林练习题1.2

  • 2026-11-07 23:31:29
徐森林练习题1.2题目
练习题1.2答案
注意：(11)我们给出了一般的形式，读者可以了解更一般的n的k次幂求和具体公式以及伯努利数的相关知识
第四题我们给出了两个常用的命题，值得注意的是这两个逆命题均不成立
第五题是华里士乘积的估计公式希望读者掌握
第六题需要大家注意的是a不可以等于0，我们举1/2的n次幂就是一个例子他开n次幂极限不为1
第七题我们给出了更一般的形式这里需要大家掌握这个epsilon是任取的，为什么要取epsilon而不是取具体的数呢例如1/2呢，事实上读者可以自行尝试一下会发现最后一步的极限是1，无法得出极限以此我们取epsilon。这样最后得到的式子小于任意的正数那它只能是0
第8题大家可以学习一下情形三数列的取法，另外此题还可以利用最大最小值公式去做这里笔者省略了
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  1. CONNECT:[ UseTime:0.000553s ] mysql:host=172.18.0.4;port=3306;dbname=www_sjds;charset=utf8mb4
  2. SHOW FULL COLUMNS FROM `fenlei` [ RunTime:0.000637s ]
  3. SELECT * FROM `fenlei` WHERE `fid` = 0 [ RunTime:0.000349s ]
  4. SELECT * FROM `fenlei` WHERE `fid` = 63 [ RunTime:0.000335s ]
  5. SHOW FULL COLUMNS FROM `set` [ RunTime:0.000536s ]
  6. SELECT * FROM `set` [ RunTime:0.000274s ]
  7. SHOW FULL COLUMNS FROM `article` [ RunTime:0.000571s ]
  8. SELECT * FROM `article` WHERE `id` = 540730 LIMIT 1 [ RunTime:0.000320s ]
  9. UPDATE `article` SET `lasttime` = 1794067002 WHERE `id` = 540730 [ RunTime:0.001096s ]
  10. SELECT * FROM `fenlei` WHERE `id` = 65 LIMIT 1 [ RunTime:0.000310s ]
  11. SELECT * FROM `article` WHERE `id` < 540730 ORDER BY `id` DESC LIMIT 1 [ RunTime:0.000448s ]
  12. SELECT * FROM `article` WHERE `id` > 540730 ORDER BY `id` ASC LIMIT 1 [ RunTime:0.000363s ]
  13. SELECT * FROM `article` WHERE `id` < 540730 ORDER BY `id` DESC LIMIT 10 [ RunTime:0.000479s ]
  14. SELECT * FROM `article` WHERE `id` < 540730 ORDER BY `id` DESC LIMIT 10,10 [ RunTime:0.000505s ]
  15. SELECT * FROM `article` WHERE `id` < 540730 ORDER BY `id` DESC LIMIT 20,10 [ RunTime:0.000562s ]
0.102097s