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This question is often asked because it seems counterintuitive that a number raised to an infinitely large power would approach a specific value.
Euler's number, e, is a mathematical constant that arises frequently in calculus, and it represents the base of the natural logarithm. In this equation, it is the limit that (1+1/n)^n approaches as n becomes infinitely large.
The equation (1+1/n)^n approaching e as n approaches infinity has many practical uses, such as in compound interest calculations, population growth models, and radioactive decay calculations. It is also used in various fields of science, including biology, physics, and economics.
Yes, there are multiple proofs for this equation, including using the binomial theorem, the definition of limits, and the definition of e itself as the limit of (1+1/n)^n as n approaches infinity.
As n approaches infinity, the value of (1+1/n)^n approaches e, but it never actually reaches it. There is always a small margin of error, which can be made arbitrarily small by choosing a large enough value for n. This is a fundamental concept in calculus known as a limit.
