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A triangular number is a number that can be represented as a triangle with dots. The nth triangular number is given by the formula: \[ T_n = \frac{n(n+1)}{2} \] Write a Python function `find_index(n)` that finds the index of the smallest triangular number with exactly `n` digits. #### Example Usage ```python [main.nopy] find_index(2) # Output: 4 find_index(3) # Output: 14 find_index(4) # Output: 45 ``` #### Constraints - The input `n` will be a positive integer. - The function should return the smallest index `k` such that the triangular number \( T_k \) has exactly `n` digits.
import math def find_index(n): """ Find the index of the smallest triangular number with exactly n digits. Args: n (int): The number of digits. Returns: int: The index of the smallest triangular number with n digits. """ # Placeholder for the solution pass