and for our sum of the geometric series A/1 - r we get:

We created a geometric series with sum A/1-r, in which [alpha] does not appear!

Once again we can now do a geometric series with A = L/2 and r = 1/[square root of 2] to get the path length of this jagged spiral to be

Similar trends were found with regard to the relative abundance distributions of families and FFG: both taxonomic units fitted the stochastic normal and

geometric series models best, while FFG also fitted the random fraction model.

Traditionally, geometric series played a key role in the early development of calculus, but today, the geometric series have many key applications in medicine, computational biology, informatics, etc.

In general, a geometric series is the sum of the terms of the geometric sequence:

+ [r.sup.[n - 1]].In the geometric series, the first term shows a = 1.

In the four classical models soon to be described, we see that the dominance pattern steadily increases from the broken-stick to the truncated log-normal, logarithmic and geometric series.

The geometric series (Motomura, 1932) was proposed for benthos communities in lakes.

Here, we intend to introduce the convolution of two

geometric series. For this, let

The problem is interesting, because there are close relationship between the Smarandache multiplicative sequence and the

geometric series. In this paper, we shall use the elementary method to study the convergent properties of some infinite series involving the Smarandache multiplicative sequence, and get some interesting results.

Among specific topics are Archimedes and the

geometric series to be, the binomial series in the hands of Euler, the Cauchy product, welcome to irrationals: the complete space of real numbers, and features of Ces[sz]ro and Abel means.