Tag Archives: convergence

3 Sequences videos

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In this post we will learn about sequences of real numbers. Sequence in itself is a function with domain as the set of Natural numbers and the co-domain as the set of real numbers.

The first video defines sequences using the epsilon- neighborhood explanation method. It will explain us the existence of a limit of a sequence.

In the second video we shall learn about some examples of different type of sequences and finally in the last video we will prove that any real sequence can tend towards only one limit say L, and that L has to be unique. Continue reading →

4 Convergence of sequences videos

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Now that we know what are sequences and what do we mean by the limit of any sequence we shall learn different ways to express the same. Hence in the first video we will learn about various definitions for convergence of a sequence and understand how they are equivalent.

In the second video we will use the epsilon definition in order to find the limit of some sequences and in the third video we will try to understand an m tail sequence out of any sequence and how if a sequence converges the limits should be the same for m-tail and original sequence.

In the last video of this post we shall understand the sandwich theorem for sequences just like we have learnt for limits of any function. Continue reading →