euler’s number ‘e’ is a numerical constant used in mathematical calculations. the value of e is 2.718281828459045… and so on. like pi(π), e is also an irrational number. it is basically described under concepts of logarithms. ‘e’ is a mathematical constant, which is basically the base of the natural logarithm. this is an important constant that is used not only in mathematics but also in physics. also called Eulerian number or Napier’s constant.
‘e’ is primarily used to represent the non-linear increase or decrease of a function such as population growth or decrease. the main application can be seen in the exponential distribution.
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value of e raised to 1 (e1) will give the same value as e but the value of e raised to 0 (e0) is equal to 1 and e raised to infinity gives the value 0. it is a unique and special number, whose logarithm gives the value 1, that is,
log e = 1
In this article, we will learn how to evaluate the value of Euler’s number.
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euler number (e)
the euler number ‘e’, is the limit of (1 + 1/n)n as n approaches infinity, an expression that arises in the study of compound interest. can also be expressed as the sum of infinite numbers.
The value of the constant e can be calculated by solving the previous expression. this will result in an irrational number, which is used in various mathematical concepts and calculations.
Similarly, like other mathematical constants like β, π, γ, etc., the value of the constant e also plays an important role. the number e, have similar properties just like other numbers. we can operate all the mathematical operations, using the value of the logarithm base e.
what is the value of e in mathematics?
as discussed above, jacob bernoulli discovered the mathematical constant e. the expression, given as the sum of infinities for euler’s constant, e, can also be expressed as;
therefore, the value of (1+1/n)n reaches e when n reaches ∞. If we put the value of n in the above expression, we can calculate the approximate value of the number e. so, let’s start putting the value of n =1 to higher digits.
why is it important
The exponential constant is a significant mathematical constant and is denoted by the symbol ‘e’. is approximately equal to 2.718. this value is frequently used to model physical and economic phenomena, mathematically, where it is convenient to write e. the exponential function can be easily described using this constant, for example, y = ex, so that as the value of x changes, we can calculate the value of y.
total value of e
the value of the euler number has a large number of digits. can go to a place of 1000 digits. But in mathematical calculations, we use only the approximate value of Euler’s number e, equal to 2.72. the first few digits of e are given here though:
e = 2.718281828459045235360287471352662497757247093699959574966967627724076630353………..
how to calculate the value of e?
So far we have learned about the mathematical constant or Euler’s constant or base of the natural logarithm, e and the values of e. the expression for e to calculate its value was given as;
Now, if we solve the previous expression, we can find the approximate value of the constant e.
e = 1/1 + 1/1 + 1/2+ 1/6 + 1/24 + 1/120 + ……
now, taking only the first few terms.
e = 1/1 + 1/1 + 1/2+ 1/6 + 1/24 + 1/120
e = 2.71828
therefore, the value of e is equal to 2.71828 or e ≈ 2.72.
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