Question

Find a formula for f(x)
f(2) = (1/2)^0 +(1/2)^1 + (1/2)^2 = 1+ 1/2+1/4=7/4

Answer 1

What is the original function?

Answer 2

I can't understand the question

Answer 3

let f(x) be a function that adds the first x powers of 1/2 and then find the function with this given info.

Answer 4

Let f(x) be a function that adds the first x powers of 1/2:
f(x) = (1/2)^0 = 1
f(1) = (1/2)^0 + (1/2)^1 = 1+1/2 =3/2
f(2) = (1/2)^0 +(1/2)^1 + (1/2)^2 = 1+ 1/2+1/4=7/4

Answer 5

Is this supposed to go on to infinity? i.e \[\sum_{x=0}^{\infty}\left( \frac{1}{2}\right)^x \]

Answer 6

how do i express that in terms of f(x) ?

Answer 7

maybe you could use a recursive definition

\( f(x_0)=1/2\\
f(x_n)=f(x_{n-1})+1/2\)