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Algebra
Published in H. G. Davies, G. A. Hicks, Mathematics for scientific and technical students, 2014
Besides common logarithms to the base 10 there is another type oflogarithm which is extremely important in science and engineering, called natural or Napierian logarithms. The base of these logarithms is the number e, where e is defined by the series e=1+12+11×2+11×2×3+11×2×3×4+⋅⋅⋅=1+1+0.5+0.16667+0.04167 The terms decrease sufficiently rapidly for the sum of the series to reach a limiting value as the number of terms becomes very large. The limiting value correct to three places of decimals is 2.718. A series such as this, whose sum reaches a limiting value as the number of terms extends to infinity, is called a convergent series. In other words the sum of the series converges to a limiting value.
Posing problems and solving self-generated problems: the case of convergence and divergence of series
Published in International Journal of Mathematical Education in Science and Technology, 2023
Özkan Ergene, Büşra Çaylan Ergene
Another difficulty based on series was the use of divergent and convergent series interchangeably. In the first of the two examples given below, the divergent series was used instead of the convergent series. In the second example, the convergent series was used instead of the divergent series. In a squash practice, the ball is thrown from 20 meters away. The ball travels twice as far each time it comes back. How far does the ball travel?A bee makes a certain amount of honey every day. It makes 1 gram on the first day, gram on the second day, gram on the third day … gram on the nth day. How many grams of honey does this bee make in total?
Consensus control of leader-following nonlinear multi-agent systems with distributed adaptive iterative learning control
Published in International Journal of Systems Science, 2018
Xiongfeng Deng, Xiuxia Sun, Ri Liu, Shuguang Liu
A convergent series sequenceis defined aswhere,andare the parameters to be designed.