### 使用Python实现递推公式 \( b = 1 - n \cdot a \) 为了实现基于递推公式的计算，可以按照以下方法编写程序。此方案允许用户输入循环次数以及初始值 \( a_0 \)，随后根据给定的递推关系逐步计算每一项。 #### 初始化与递推逻辑 首先设定变量 \( a \) 初值为用户提供之值，并初始化计数器用于控制迭代轮次。接着，在指定范围内运行循环体，每一轮依据当前 \( a \) 计算新的 \( b \)，再令 \( a \) 更新为此新值得到下一回合所需资料[^1]。 以下是完整的 Python 实现： ```python def recursive_formula(initial_value, iterations): """ Perform iterative calculation based on the formula b = 1 - n * a. Args: initial_value (float): The starting value of 'a'. iterations (int): Number of times to perform the recursion. Returns: list: A list containing all computed values during each iteration. """ results = [] # List to store intermediate results for review or further processing needs a = initial_value # Initialize variable with user-provided start point for n in range(1, iterations + 1): # Begin iterating as per requested amount by caller b = 1 - n * a # Apply given recurrence relationship here directly results.append(b) # Save outcome into collection structure defined earlier a = b # Prepare next round data setup accordingly now return results # After finishing entire process deliver final outcomes back if __name__ == "__main__": try: init_val = float(input("Enter the initial value for 'a': ")) num_iters = int(input("Enter the number of iterations: ")) output_values = recursive_formula(init_val, num_iters) print("\nComputed Values:") for idx, val in enumerate(output_values, start=1): print(f"Iteration {idx}: Value = {val}") except ValueError: print("Invalid input! Please ensure you enter numeric types only.") ``` 这段脚本定义了一个名为 `recursive_formula` 的函数负责核心运算部分，接收两个参数分别是初识数值和重复执行步数。通过标准库中的异常捕捉机制保障了基本错误处理能力，使得即使面对非法字符也能优雅降级而非崩溃退出[^2]。 --- ###