From Integrable Functions To Limits Of Sequences
Teodor-Dumitru Vălcan · The European Proceedings of Social & Behavioural Sciences · 2018
The formation and development of methodological competences to apply mathematical knowledge to solving exercises and problems must be one of the fundamental objectives of each Mathematics teacher. Unfortunately this is very rare, precisely because professors do not have such competences. This paper aims to be an example of training and developing these competences for a very sensitive field: the calculation of the limits of sequences by special methods, more precisely with the help of definite integrals. It is known that certain limits of convergent sequences can be calculated using definite integrals. On the other hand, any function f integrable over an interval [a,b] induces a convergent sequence, that of the Riemann sums, which converges to the value of the integral of f on [a,b]. In this paper we show that in addition to this sequence, such a function f, which takes only positive values, may also lead to two more convergent sequences, and the calculation of their limits is also reduced to the calculation of the integral of f over the interval [a,b]. The idea is that through the results and examples presented here to increase the sphere of the methodological competences of pupils / students to calculation of limits of convergent sequences