1. Write a function that takes a sorted list and a target value, and returns the index where the target can be inserted to maintain the order, placing it to the left of any existing duplicates.
2. Create a function that checks if a given string starts with a vowel using a regular expression and returns "Valid" or "Invalid" accordingly.
3. Define a recursive function that computes the geometric sum of powers of 1/2 from 2⁻⁰ to 2⁻ⁿ for a given n.
4. Write a Python function that returns the index of the smallest triangular number that has exactly n digits.
5. Convert a tuple into a dictionary by pairing every two adjacent elements as key-value pairs in a new function.
