E facts & stats

Question 1

e is an irrational number. What does that mean?

Accepted Answer

Its decimal digits never end or repeat. Irrational numbers cannot be written as a fraction of whole numbers, so their decimals go on forever without repeating.

Question 2

The natural logarithm uses which number as its base?

Accepted Answer

e. The natural logarithm, written ln, is the logarithm to base e.

Question 3

What is the derivative of e^x?

Accepted Answer

e^x. e^x is the special function that is its own derivative, so its slope at any point equals its value.

Question 4

As n gets larger and larger, (1 + 1/n)^n gets closer to which number?

Accepted Answer

e. The expression (1 + 1/n)^n approaches e as n grows without limit: for n = 1,000 it is already about 2.717.

Question 5

What is the sum 1 + 1/1! + 1/2! + 1/3! + 1/4! + … equal to?

Accepted Answer

e. The infinite series of 1 over each factorial adds up to e, which is one common way to calculate it.

Question 6

Euler's identity states that e^(iπ) + 1 equals what?

Accepted Answer

0. Euler's identity, e^(iπ) + 1 = 0, links e, i, π, 1 and 0 in one equation.

Question 7

Like e, which of these numbers is transcendental?

Accepted Answer

π. π is transcendental like e; √2 is irrational but algebraic, while 22/7 and 1.5 are rational.

E facts & stats

The basics