The concept of Euler's number can be very tedious, so make sure to pay attention while reading. The concept of e can be really tricky to understand, partially because it is an irrational number, and partially because it can be expressed with a formula that is lengthy. If you do not know about summation notation, be sure to read the article, Introduction to Summations.
ISAIAH LOPEZ
The letter e is used in math to represent Euler's number. Euler was just the mathematician who discovered the number. If you are familiar with the number pi, you probably know that it is irrational. This means that it cannot be expressed as a ratio between two integers or written as a fraction. The value of pi is approximately 3.14159265, but the digits keep continuing forever and never repeat in a pattern. Similar to pi, e is also an irrational number and its value is approximately 2.71828182 Again, it never repeats in a predictable way and the digits continue forever.
Although e is irrational and somewhat "unpredictable", it still has a formula that is surprisingly made up of rational numbers. The formula for e is the sum of the reciprocals of the factorials of all the whole numbers. This might sound complicated, but when it is written in summation notation, it becomes easier to understand. For review, a factorial is the product of a whole number and every whole number that comes before it. For example, 4! = 4 ⋅ 3 ⋅ 2 ⋅ 1.
This equation is simply 1/0! + 1/1! + 1/2! + 1/3! + 1/4!, and so on. Also remember that 0! is equal to 1, so the equation starts with 1 + 1 + 0.5 + other decimal numbers that will eventually add up to Euler's number. Something to note is that the value of e never reaches three. It remains at 2 followed by a decimal, meaning that no matter how many numbers are added in the series, the value will never reach 3 and will approach e.
In conclusion, e is the sum of the reciprocals of the factorials of the whole numbers. It can be tricky to understand, but a good understanding of both factorials and summations is helpful. Remember that since e is an irrational number, it will never end and just like pi, all digits cannot be memorized. If you do not know about factorials, check out the article, Introduction to Factorials, and if you do not know about summations, check out the other article, Introduction to Summations.