ABSTRACT
If |r| < 1, then the infinite geometric series a1(1 + r + r2 + r3 + · · · ) converges to a1 1−r . For example, 1 +
1 8 + · · · = 2.
2.1.2.3 Means 1. The arithmetic mean of a and b is given by a+b2 . More generally, the arithmetic
mean of a1, a2, . . . , an is given by (a1 + a2 + · · ·+ an)/n. 2. The geometric mean of a and b is given by
√ ab. More generally, the geometric
mean of a1, a2, . . . , an is given by n √ a1a2 . . . an. The geometric mean of n
numbers is less than the arithmetic mean, unless all of the numbers are equal. 3. The harmonic mean of a and b is given by 11
( 1 a +
) = 2ab a+ b
.
