几何级数

With the development of information technology and communication technology, the issue of timeliness becomes more prominent today when the amount of information is increasing in a geometrical progression.

随着信息技术及通信技术的发展，时效性问题在信息量呈几何级数增长的今天，显得更加突出。

It is only by assuming an infinitely small magnitude, and a progression rising from it up to a tenth, and taking the sum of that geometrical progression, that we can arrive at the solution of the problem.

只有假设出无穷小数和由无穷小数产生的十分之一以下的级数，再求出这一几何级数的总量，我们才能得出问题的答案。

This takes an order of magnitude more work.

这将以更多成几何级数的工作量作为代价。

Shoe of sponge cake bottom (before palm 50 Mm above person) the addition as ply, curve stress to show geometrical progression to increase, some resembles board shoe same, essential.

松糕底鞋（前掌50mm以上者）随着厚度的增加，弯曲应力呈几何级数增大，有的就像木板鞋一样，根本。。。

For example, geometric series can be used to evaluate the sum of power series and can be used to determine the convergence of other series.

例如可以用几何级数来解决幂级数的求和问题、以及用它作为优级数来判定其他级数的收敛性等等。

One of them contains a special case of q-Dougall summation formula,the other includes the famous Rogers-Ramanujan identities as special cases.

我们发现了两类新的基本超几何级数求和变换公式，其中一类的特殊情况包含在q-Dougall的求和公式中，另一类的特殊情况是著名的Rogers-Ramanujan恒等式。

Via generalizing the Cauchy method we obtain a new method,called the modified Cauchy method.By means of this method we establish two bilateral _3ψ_3 and _4ψ_4 series summation formulae,two four-term summation and transformation formulae for unilateral _3φ_2-series and bilateral _3ψ_3-series,and two five-term summation and transformation formulae for unilateral _3φ_2-series and bilateral _3φ_3-series,which contain many known results as their special cases,such as non-terminating q-Saalschütz summation formula,Bilateral _6ψ_6 series summation formula of Bailey,non-terminating Watson transformation formula and some transformations of _3φ_2-series etc.

通过对Cauchy方法的推广，我们得到修正的Cauchy方法，采用这个方法分别得到两个双边的_3ψ_3和_4ψ_4基本超几何级数的求和公式、单边_3φ_~(2-)级数和双边_3ψ_(3~-)级数的两个四项求和变换公式和两个五项求和变换公式，它们包括许多已有的结果为特例，如非终止的q-Saalschütz求和公式、Bailey的very-well-poised双边级数_6ψ_6求和公式、非终止的Watson变换公式和一些关于单边_3φ_(2~-)级数的变换公式等。

The results showed that the quantities of plant parasitic nematodes of Aphelenchoides and Aphelenchus increased at a speed of geometric order after one growing season,which indicated that the two kinds of nematodes had highly potential risk.

研究结果表明栽培前种球内的优势植物线虫——拟滑刃属和滑刃属线虫数量在百合一个生长周期结束后均以几何级数的速率增长；栽培前检出数量极少的垫刃属线虫，生长周期结束后却大量出现；栽培前少量检出的短体属、矮化属、根结属、丝尾垫刃属和伪垫刃属的线虫，周期结束后，均未再检测到。

A contract with an inconsiderate contractee for the delivery of 32 consignments of some given commodity in consideration of cash payment on delivery per delivery at the initial rate of 1/4d to be increased constantly in the geometrical progression of 2 (1/4d, 1/2d, 1d, 2d, 4d, 8d, 1s 4d, 2s 8d to 32 terms).

与一个粗心的订约者签订一份商业合同：作为三十二件商品的运送费，第一件只收四分之一便士，自第二件起，以二的几何级数递增（四分之一便士，二分之一便士，一便士，二便士，四便士，八便士，一先令四便士，二先令八便士，一直递增到第三十二件）。

With the development of the information era, the quantity of information increases in the way of geometric series, and people find that it is more and more difficult to obtain valuable informatin and it is incogitable to find out the rules hiding in the information.

随着信息时代的发展，信息量呈几何级数增长，人们发现从这些海量信息中获取有用的信息越来越困难，要找出信息背后隐藏的规律更是不可想象。

For a big chunk of credit-card losses; the number of filings (and thus charge-off rates) would be rising again, whether

年美国个人破产法的一个改动使得破产登记急速下降，而后引起了信用卡大规模的亏损。

Eph. 4:23 And that you be renewed in the spirit of your mind

弗四23 而在你们心思的灵里得以更新