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Date: Thu, 19 Jun 2025 20:20:44 +0800
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---
 .idea/inspectionProfiles/极限与级数.py | 171 ++++++++++++++++++++
 1 file changed, 171 insertions(+)
 create mode 100644 .idea/inspectionProfiles/极限与级数.py

diff --git a/.idea/inspectionProfiles/极限与级数.py b/.idea/inspectionProfiles/极限与级数.py
new file mode 100644
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+++ b/.idea/inspectionProfiles/极限与级数.py
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+#数列极限计算、数列敛散性判定、部分和数列计算、级数敛散性判定
+
+from sympy import*
+from convert_formula import *
+
+def calculate_sequence_limit(sequence, n=1, tolerance=1e-10, max=1000):
+    """
+    数列极限求和并判断敛散性
+    :param sequence: 数列通式
+    :param n:开始计算的n值
+    :param tolerance:判断收敛的容差
+    :param max: 最大计算项数
+    :return:数列极限
+    """
+    prev_term = sequence(n)
+    current_term = sequence(n + 1)
+
+    #判断当n足够大时，第n项与第n+1项是否相等
+    for i in range(n + 2, n + max + 1):
+        if abs(current_term - prev_term) < tolerance:
+            return current_term,True
+
+        pre_term = current_term
+        current_term = sequence(i)
+
+    return None,False
+
+def calculate_partial_sums(series_term, n_terms):
+    """
+    部分和数列求和
+    :param series_term:数列通式
+    :param n_terms:总共求和的项数
+    :return:数列和
+    """
+    #将数列前n项求和
+    sum_list=[]
+
+    for i in range(n_terms):
+        sum_list.append(series_term(i))
+
+    return sum(sum_list)
+
+def is_series_convergent(series_term, n=1, tolerance=1e-10, max=1000):
+    """
+    判断级数敛散性
+    :param series_term: 数列通式
+    :param n: 开始计算的n值
+    :param tolerance: 判断收敛的容差
+    :param max: 最大计算项数
+    :return: True/False
+    """
+    #首先检查通项极限是否为0
+    def term_sequence(n):
+        return series_term(n)
+
+    limit, converged = calculate_sequence_limit(term_sequence, n, tolerance, max)
+
+    if converged and abs(limit) > tolerance:
+        return False  # 通项极限不为0，级数发散
+
+    #判断部分和和数列是否收敛
+    def partial_sum_sequence(k):
+        return sum(sum_list)
+
+    limit,sum_converged = calculate_sequence_limit(partial_sum_sequence, n, tolerance, min(max_terms // 2, 100))
+
+    return sum_converged
+
+
+# 测试函数
+def run_tests():
+    print("===== 数列与级数计算库测试 =====")
+
+    # 测试数列极限计算
+    def test_sequence_limit():
+        # 收敛数列 1/n
+        def seq1(n):
+            return 1 / n
+
+        limit, converged = calculate_sequence_limit(seq1)
+        print(f"数列 1/n: 极限={limit}, 收敛={converged}")
+
+        # 发散数列 n
+        def seq2(n):
+            return n
+
+        limit, converged = calculate_sequence_limit(seq2)
+        print(f"数列 n: 极限={limit}, 收敛={converged}")
+
+    # 测试数列敛散性
+    def test_sequence_convergence():
+        # 收敛数列 (-1)^n/n
+        def seq1(n):
+            return (-1) ** n / n
+
+        converged = is_sequence_convergent(seq1)
+        print(f"数列 (-1)^n/n: 收敛={converged}")
+
+        # 发散数列 sin(n)
+        def seq2(n):
+            import math
+            return math.sin(n)
+
+        converged = is_sequence_convergent(seq2)
+        print(f"数列 sin(n): 收敛={converged}")
+
+    # 测试部分和计算
+    def test_partial_sums():
+        # 等比级数 1/2^n
+        def term(n):
+            return 1 / (2 ** n)
+
+        sums = calculate_partial_sums(term, 5)
+        print(f"级数 1/2^n 的前5项部分和: {sums}")
+
+    # 测试级数敛散性
+    def test_series_convergence():
+        # 收敛级数 1/n^2
+        def term1(n):
+            return 1 / (n ** 2)
+
+        converged = is_series_convergent(term1)
+        print(f"级数 1/n^2: 收敛={converged}")
+
+        # 发散级数 1/n
+        def term2(n):
+            return 1 / n
+
+        converged = is_series_convergent(term2)
+        print(f"级数 1/n: 收敛={converged}")
+
+    # 执行所有测试
+    test_sequence_limit()
+    print()
+    test_sequence_convergence()
+    print()
+    test_partial_sums()
+    print()
+    test_series_convergence()
+def UI():
+    command=input('请选择功能：1.数列极限并判断敛散性 2.部分和数列求和 3.判断级数敛散性')
+    if command=="1":
+        sequence=input('请输入以n为变量的数列通式（如1/n）：')
+        limitation,convergent=calculate_sequence_limit(sequence, n=1, tolerance=1e-10, max=1000)
+        if convergent:
+            print(f"数列收敛，极限值为{limitatoion}")
+        else:
+            print('极限不存在')
+
+    elif command=='2':
+        series_term = input('请输入以n为变量的数列通式（如1/n）：')
+        n_term= input('请输入计算项数：')
+        result= calculate_partial_sums(series_term, n_terms)
+        print(f'通式为{series_term}前{n_term}项和为{result}')
+    elif command=='3':
+        series_term = input('请输入以n为变量的数列通式（如1/n）：')
+        result=is_series_convergent(series_term, n=1, tolerance=1e-10, max=1000)
+        if result:
+            print('该级数收敛')
+        else:
+            print('该级数发散')
+
+if __name__ == "__main__":
+    main_menu()
+
+
+
+
+
+
+