- #1
eddybob123
- 178
- 0
well, i kno that e is derived from (1+(1/n))^n, as n goes to infinity, but i want to find a finite series . if i plot a curve like this on a graph, then take its derivative, i can tske a value of e.
eddybob123 said:well, i kno that e is derived from (1+(1/n))^n, as n goes to infinity, but i want to find a finite series . if i plot a curve like this on a graph, then take its derivative, i can tske a value of e.
Any finite series, involving only integers and fractions of integers, must give a rational number. e is not rational so there can be no such finite series. In fact, because e is transcendental, any such series would have to involve transcendental numbers as coefficients which would be as difficult to work with as e itself.eddybob123 said:well, i kno that e is derived from (1+(1/n))^n, as n goes to infinity, but i want to find a finite series . if i plot a curve like this on a graph, then take its derivative, i can tske a value of e.
Euler's number, denoted as e, is a mathematical constant that is approximately equal to 2.71828. It is an important number in mathematics and has many applications in calculus, statistics, and other areas of mathematics.
Euler's number is calculated as the limit of the expression (1 + 1/n)^n as n approaches infinity. This means that as n gets larger and larger, the value of (1 + 1/n)^n gets closer and closer to the value of e. This expression is also equivalent to the sum of the infinite series 1 + 1/1! + 1/2! + 1/3! + ..., which can be used to approximate the value of e.
The finite series for Euler's number is a sum of a finite number of terms that approach the value of e. It can be written as 1 + 1/1! + 1/2! + 1/3! + ... + 1/n!, where n is the number of terms in the series. As n approaches infinity, the value of this finite series gets closer and closer to the value of e.
The number of terms needed to accurately approximate e depends on the desired level of accuracy. Generally, the more terms included in the series, the more accurate the approximation will be. However, even with a small number of terms, the finite series can provide a close approximation of e.
Euler's number has many real-life applications, including in compound interest, population growth, and radioactive decay. It is also used in the fields of physics, engineering, and economics to model various phenomena. Additionally, e is used in the study of logarithms and complex numbers, and in the development of algorithms and computer programs.