Question

What will be the sequence generated by the generating function 4x/(1-x)2 ​

Answer 1

Given:

The function 4x/(1-x)2 ​

To find:

What will be the sequence generated by the generating function 4x/(1-x)2 ​

Solution:

From given, we have a function,

4x/(1-x)2

The sequence generated by this function depends on the input value.

We cannot substitute, x = 1, as the denominator equals to infinity.

Considering, the numbers from 2 to n are entered, then we have the sequence given by,

when, x = 2

4x/(1-x)2 ⇒ 4(2)/(1-2)2 = 8/(-1)2 = 8

when, x = 3

4x/(1-x)2 ⇒ 4(3)/(1-3)2 = 12/(-2)2 = 3

when, x = 4

4x/(1-x)2 ⇒ 4(4)/(1-4)2 = 16/(-3)2 = 16/9

and so on...

Therefore, the sequence is, 8, 3, 16/9,.........