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Q: How you find the order of convergence of a series?
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What is convergence of probability?

"Convergence in probability" is a technical term in relation to a series of random variables. Not clear whether this was your question though, I suggest providing more context.


What is the rate of convergence for the bisection method?

The rate of convergance for the bisection method is the same as it is for every other iteration method, please see the related question for more info. The actual specific 'rate' depends entirely on what your iteration equation is and will vary from problem to problem. As for the order of convergance for the bisection method, if I remember correctly it has linear convergence i.e. the convergence is of order 1. Anyway, please see the related question.


Why is calculus important to trigonometry?

In advanced mathematics, familiar trigonometric ratios such as sine, cosine or tan are defined as infinite series. For example, sin(x) = x - x3/3! + x5/5! - ... Such series are used to calculate trig ratios and the proof of their their convergence to a specific value depends on calculus.


What factors determines the region of convergence of a z transform?

The region of convergence (ROC) of x(z) is the set of all values of z for which x(z) attains a finite value.


What are the famous mathematical problems involving pie?

In the beginning of the 20th century, the Indian mathematician Srinivasa Ramanujan found many new formulas for π, some remarkable for their elegance, mathematical depth and rapid convergence.[58] One of his formulas is the series,