Some more average numbers

Number Theory Level pending

Let $x_0, x_1, x_2,\ldots$ be a sequence of a numbers satisfying the recursion,

$x_{n} =\dfrac{x_{n-1} + x_{n-2}}2 ,$

where $n = 2,3,4 \ldots$ .

If $x_0 = 0$ and $x_1 = 1890$ , find the following:

$\lim_{n \rightarrow \infty} x_n$

1 solution

Geoff Pilling
Jul 30, 2016

$\lim_{n\to \infty} x_n = 1980 \times \sum_{n=0}^{\infty} (-1/2)^n= 1980 \times \frac{2}{3} = \boxed{1260}$

What do you mean by "The sequence is equivalent to a number"?

Great question. There is a simple way of writing out what each of these terms should be.

Calvin Lin Staff - 4 years, 10 months ago

Yeah, I had a bit of unnecessary verbiage... There, I've removed it... :)

Geoff Pilling - 4 years, 10 months ago