增添若干自拟题目

题库0.3/Problems.json

@@ -612306,6 +612306,106 @@
         "space": "",
         "unrelated": []
     },
+    "022933": {
+        "id": "022933",
+        "content": "求下列各式的值:\\\\\n(1) $\\displaystyle\\lim_{n \\to +\\infty}(\\dfrac{1}{2}+\\dfrac{1}{4}+\\cdots+\\dfrac{1}{2^n})=$\\blank{50};\\\\\n(2) $\\displaystyle\\lim_{n \\to +\\infty}(\\dfrac{1}{3}-\\dfrac{1}{9}+\\cdots+(-1)^{(n+1)}\\dfrac{1}{3^n})=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20231211\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "022934": {
+        "id": "022934",
+        "content": "将下列循环小数化为分数:\\\\\n(1) $0.\\dot{3}2\\dot{5}$;\\\\\n(2) $2.6\\dot{4}\\dot{5}$.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20231211\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "022935": {
+        "id": "022935",
+        "content": "将以下四则运算的结果用最简表示:\\\\\n(1) $0.\\dot{6}+1.\\dot{7}$;\\\\\n(2) $0.3\\times 0.\\dot{3}\\times 0.\\dot{3}\\dot{3}$.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20231211\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "022936": {
+        "id": "022936",
+        "content": "已知数列$\\{a_n\\}$的通项公式为$a_n=n^2-5n+1$, 分析该数列的单调性, 并求其最小项的序数.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20231211\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "022937": {
+        "id": "022937",
+        "content": "已知数列$\\{a_n\\}$满足: $a_1=-2$, $a_{n+1}=a_n^2+2$($n\\in \\mathbf{N}$, $n\\ge 1$), 判断该数列的单调性, 并证明你的结论.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20231211\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
     "030001": {
         "id": "030001",
         "content": "若$x,y,z$都是实数, 则:(填写``\\textcircled{1} 充分非必要、\\textcircled{2} 必要非充分、\\textcircled{3} 充要、\\textcircled{4} 既非充分又非必要''之一)\\\\\n(1) ``$xy=0$''是``$x=0$''的\\blank{50}条件;\\\\\n(2) ``$x\\cdot y=y\\cdot z$''是``$x=z$''的\\blank{50}条件;\\\\\n(3) ``$\\dfrac xy=\\dfrac yz$''是``$xz=y^2$''的\\blank{50}条件;\\\\\n(4) ``$|x |>| y|$''是``$x>y>0$''的\\blank{50}条件;\\\\\n(5) ``$x^2>4$''是``$x>2$'' 的\\blank{50}条件;\\\\\n(6) ``$x=-3$''是``$x^2+x-6=0$'' 的\\blank{50}条件;\\\\\n(7) ``$|x+y|<2$''是``$|x|<1$且$|y|<1$'' 的\\blank{50}条件;\\\\\n(8) ``$|x|<3$''是``$x^2<9$'' 的\\blank{50}条件;\\\\\n(9) ``$x^2+y^2>0$''是``$x\\ne 0$'' 的\\blank{50}条件;\\\\\n(10) ``$\\dfrac{x^2+x+1}{3x+2}<0$''是``$3x+2<0$'' 的\\blank{50}条件;\\\\\n(11) ``$0<x<3$''是``$|x-1|<2$'' 的\\blank{50}条件.",