Question

Is there a closed form solution for B in terms of x_i's and n?:
(see below)

Answer 1

\[\frac{ \sum_{i=1}^{n}i*x_i*B^{2i}}{ \sum_{i=1}^{n}i*B^{i} } = \frac{ \sum_{i=1}^{n}x_i*B^{i}}{ \sum_{i=1}^{n}B^{2i} } \]

Answer 2

So you have B^2i on the top on the left hand side, but B^2i on the bottom on the right hand side.... is that on purpose?

Answer 3

Oops. My mistake. The numerators should have B^i and the denominators should have B^2i in them.

Answer 4

\[\frac{ \sum_{i=1}^{n} i*x_i * B^{i} }{\sum_{i=1}^{n} i* B^{2i}} = \frac{ \sum_{i=1}^{n} x_i * B^{i} }{\sum_{i=1}^{n} B^{2i}}\]

Answer 5

\(B\) is a complex number?

Answer 6

Nope. It's basically a ratio. Should be close to 1 for my purposes.

Answer 7

(very heartening to hear you correct my question, though)

Answer 8

If it help, it should be reasonably well approximated by some averaging of:
\[B \approx mean \frac{x_{i+1}}{x_i}\]

Answer 9

Lol, if you are to do that, you should probably just give me the whole question. Else I'll just assume B is a constant. In the case that B is a constant, as far as I know, the top cannot be simplified, but the bottom is just a geometric sum. Do you know how to simplify a geometric sum?

Answer 10

B is a constant

Answer 11

I can simplify the second denominator; not so clearly on the first although I guess I've probably done that before.