The spell grew geometrically, as it rippled through the air.

咒语在空气中扩散，何级数增长着。

One approach involves adding up every chance the human has to win, using geometric series.

种方法是通使用何级数，将人类获胜种可能性相加。

The robot's total probability is also the total of a geometric series.

机器人总概率也是个何级数总和。

We could bypass geometric series by starting with this reasoning.

我们可以通以下推理来绕何级数。

Perhaps geometrically increased, and that's very unlikely to slow down.

或许何级数增长，而且这非常不可能会放缓。

Beyond that the difficulty of solving them rises in almost geometrical progression.

除此之外，解决它们难度何级数上升。

They're called geometric series right, they're called geometric series.

它们被称为何级数，对吧，它们被称为何级数。

As one develops analytic listening skills, the opportunities to enjoy music increase geometrically.

随着分析聆听技能提高，享受音乐机会将何级数增加。

Two facts about geometric series are useful here.

关于何级数，有两个事实在这里很有用。

A geometric series is an infinite sum of numbers, where each number is the previous number multiplied by a common ratio.

何级数是指个无限数列和，其中项都是前项乘以个公比。

If we add all the possible probabilities of a human win, the total is the sum of a geometric series.

如果我们把人类获胜所有可能概率相加，总数就是何级数和。

First, if the common ratio r of a geometric series has absolute value less than 1, the series has a finite total.

首先，如果何级数公比r绝对值小于1，那么这个级数有个有限和。

Wildeve forgot the loss of the money at the sight of his lost love, whose preciousness in his eyes was increasing in geometrical progression with each new incident that reminded him of their hopeless division.

韦狄见到他失去爱人，顿时就把输钱事忘了，当新发生什么事都让他想起他们之间使人绝望分离，她那份珍贵在他眼里，就以何级数增加。