The 09th period in the periodic table is equal to 1 because it represents the first energy level of an atom. This energy level can hold a maximum of 2 electrons, which is why the 09th period starts with Hydrogen (1 electron) and Helium (2 electrons). Each subsequent period in the periodic table represents a higher energy level with more electron orbitals available for filling. **

No, the 09th period is not identical to the 1st period. In a typical context, the 09th period would occur at a later time than the 1st period, indicating a progression of time. Additionally, the activities, events, and circumstances during the 09th period would likely be different from those of the 1st period, as time has passed and new experiences have occurred. Therefore, the 09th period would not be identical to the 1st period. **

One way to prove that the 09th period converges to 1 is by showing that the difference between consecutive terms in the sequence approaches zero as n approaches infinity. This can be done by taking the limit of the sequence as n approaches infinity and showing that it equals 1. Additionally, one can use mathematical induction to prove that each term in the sequence is equal to 1. Finally, one can also use the definition of convergence to show that the sequence approaches 1 as n becomes arbitrarily large. **

Horizontal mergers can lead to economies of scale, increased market power, and the ability to eliminate competition. By combining two companies that operate in the same industry, the merged entity can benefit from cost savings and increased efficiency. On the other hand, vertical mergers can result in better control over the supply chain, reduced transaction costs, and improved coordination between different stages of production. This can lead to improved quality control, lower production costs, and increased market access. Both types of mergers can result in increased market share and potentially higher profits for the merged entity. **

In a free market economy, it can be justified to restrict market and entrepreneurial freedom through the requirement for approval in larger mergers in order to prevent monopolies and promote fair competition. Without such restrictions, larger companies could potentially use their market power to stifle competition, leading to higher prices and reduced consumer choice. By requiring approval for larger mergers, regulators can ensure that the market remains competitive and that smaller businesses have the opportunity to thrive. This can ultimately benefit consumers and the overall economy. **