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According to Jack Goldstone, "in the twentieth century, the Great Divergence peaked before the First World War and continued until the early 1970s, then, after two decades of indeterminate fluctuations, in the late 1980s it was replaced by the Great Convergence as the majority of Third World countries reached economic growth rates significantly ...
The series can be compared to an integral to establish convergence or divergence. Let f ( n ) = a n {\displaystyle f(n)=a_{n}} be a positive and monotonically decreasing function . If
In vector calculus, divergence is a vector operator that operates on a vector field, producing a scalar field giving the quantity of the vector field's source at each point. More technically, the divergence represents the volume density of the outward flux of a vector field from an infinitesimal volume around a given point.
As the D in MACD, "divergence" refers to the two underlying moving averages drifting apart, while "convergence" refers to the two underlying moving averages coming towards each other. Gerald Appel referred to a "divergence" as the situation where the MACD line does not conform to the price movement, e.g. a price low is not accompanied by a low ...
When X n converges in r-th mean to X for r = 1, we say that X n converges in mean to X. When X n converges in r-th mean to X for r = 2, we say that X n converges in mean square (or in quadratic mean) to X. Convergence in the r-th mean, for r ≥ 1, implies convergence in probability (by Markov's inequality).
While most of the tests deal with the convergence of infinite series, they can also be used to show the convergence or divergence of infinite products. This can be achieved using following theorem: Let { a n } n = 1 ∞ {\displaystyle \left\{a_{n}\right\}_{n=1}^{\infty }} be a sequence of positive numbers.
The two classical summation methods for series, ordinary convergence and absolute convergence, define the sum as a limit of certain partial sums. These are included only for completeness; strictly speaking they are not true summation methods for divergent series since, by definition, a series is divergent only if these methods do not work.
Absolute convergence is important for the study of infinite series, because its definition guarantees that a series will have some "nice" behaviors of finite sums that not all convergent series possess. For instance, rearrangements do not change the value of the sum, which is not necessarily true for conditionally convergent series.