Question

NO LINKS!!

Write an expression for the apparent nth term a_n of the sequence. (Assume that n begins with 1).
1, 1/2, 1/6, 1/24, 1/120, . . .

a_n =

Answer 1

The apparent nth term of the given sequence is given by the formula:

a_n = 1 / n!

where n! is the factorial of n, defined as the product of all positive integers less than or equal to n.

For example, the first term of the sequence is 1/1! = 1/1 = 1, the second term is 1/2! = 1/2 = 1/2, the third term is 1/3! = 1/6, and so on.

Therefore, the expression for the apparent nth term of the sequence is:

a_n = 1 / n!

Answer 2

`a_n=(1)/(n!)`

Explanation:

Given sequence:

`1,\; (1)/(2),\; (1)/(6), \; (1)/(24), \; (1)/(120), \; ...`

Analyse each term in the sequence:

`a_1=(1)/(1)=(1)/(1 * 1)=(1)/(1!)`

`a_2=(1)/(2)=(1)/(2 * 1)=(1)/(2!)`

`a_3=(1)/(6)=(1)/(3 * 2 * 1)=(1)/(3!)`

`a_4=(1)/(24)=(1)/(4 * 3 * 2 * 1)=(1)/(4!)`

`a_5=(1)/(120)=(1)/(5 * 4 * 3 * 2 * 1)=(1)/(5!)`

The exclamation mark "!" placed after a number means factorial.

It means to multiply all whole numbers from the given number down to 1. Example: 4! = 4 × 3 × 2 × 1

Therefore, the equation for the nth term of the given sequence is:

`a_n=(1)/(n!)`