Which type of partnership involves at least one partner having unlimited personal liability?

In a general partnership, at least one partner has unlimited personal liability for the debts and obligations of the partnership. This means that if the business incurs debt or faces legal actions, the personal assets of the partner(s) can be used to settle those liabilities. In a general partnership, all partners typically share in the profits, management responsibilities, and liabilities, which creates a situation where one partner's financial obligation extends beyond their investment in the business.

This structure contrasts with a limited partnership, where there are both general and limited partners; the limited partners have their liability restricted to their investment. A sole proprietorship is a business owned and operated by a single individual and doesn't involve partnerships. Lastly, a limited liability partnership provides a structure where all partners have limited personal liability, protecting their personal assets from business liabilities. Therefore, the distinguishing feature of a general partnership is the presence of at least one partner who faces unlimited personal liability, making it the correct answer.