Second, the difference:

1, with different meanings:

Geometric series is a mathematical concept, which can be expressed as a * x y, that is, the growth of x to the y power.

Compared with arithmetic progression, the growth of geometric series is more impressive.

2, said different:

Arithmetic progression: For example, the "triple" of a geometric sequence is a * 2 3, which is eight times the growth of an algebraic sequence.

Geometric series usually, x=2, which is often referred to as multiple (this value is y).

Cauchy criterion

The convergence of series is the basic problem of series theory. From the concept of convergence and divergence of series, the convergence and divergence of series is defined by the convergence and divergence of its partial sum sequence Sm. Therefore, Cauchy criterion of series convergence can be obtained from Cauchy criterion of series convergence: ∑un convergence; N, for all natural numbers p, there is | u [n+1]+u [n+2]+…+u [n+p] |