Would you please tell me how to calculate natural number e ? How that number came into being ?
The natural number e, also known as Euler's number, is a mathematical constant approximately equal to 2.71828. It is important in mathematics because it is a fundamental constant that appears in many formulas and mathematical models, including compound interest, growth and decay, and normal distributions.
The natural number e was first discovered and studied by Swiss mathematician Leonhard Euler in the 18th century. He initially called it the "base of natural logarithms" and studied its properties in relation to logarithms and exponential functions. Later, it was named after him as Euler's number.
There are several methods used to calculate the natural number e, including infinite series, continued fractions, and limits. One of the most common methods is the infinite series, which is expressed as the sum of 1/n! from n=0 to infinity. Another method is using continued fractions, where e is the limit of the sequence of convergents. Lastly, e can also be calculated using limits, such as the limit of (1+1/n)^n as n approaches infinity.
The natural number e has many real-life applications in various fields, including finance, physics, and statistics. In finance, it is used in compound interest calculations, which is the basis for many financial investments. In physics, e appears in equations related to exponential growth and decay, such as radioactive decay and population growth. In statistics, e is used in probability distributions, such as the normal distribution.
No, the natural number e cannot be calculated to an exact value because it is an irrational number, meaning it has an infinite number of non-repeating decimal places. Its decimal representation is never ending and non-repeating, making it impossible to calculate to an exact value. However, it can be approximated to any desired degree of accuracy using the various methods mentioned earlier.