Introduction to series | Sequence of partial sum to check convergence of series | Geometric series

In this lecture we discuss series introduction and relationship between series and sequence. Then we learn how to form partial sum also relate partial sum with terms of the series. We also discuss convergence of the series by using partial sum with examples. At the end we discuss geometric series and its convergence and divergence of geometric series and how to find sum of geometric series.

We already discussed brief introduction of
What Archimedean Says About Natural Numbers? Archimedean Property with proof in easy way

Real SEQUENCE, Notion of sequence, why use parenthesis for sequence, Difference Between Infinite Set and Sequence?Inductive Sequence,Constant Sequence and Fibonacci sequence with examples. Kindly find the attached link for more details

In previous video we explained Definition of Limit of a sequence in a very easy way and visualize it with the help of a Example. Check the link below for details.

We already proof uniqueness of the limit of a sequence in detail. Click the link below.

We discuss in last lecture Tails of a sequence and How tail of a sequence effects convergence of a sequence?

Step by Step proof of lim(1/1+na)=0 If a is positive .

We proof that every convergent sequence is bounded we also discuss converse of this theorem i.e Every bounded sequence is convergent is not hold with the help of counter examples.

Operation of sequences addition, subtraction, multiplication, scalar multiplication and division of sequences we also proof Convergence of X+Y, X-Y, XY and cX to x+y, x-y, xy and cx respectively if X converges x and Y converges y.

Monotone increasing and monotone decreasing sequences we also proof monotone convergence theorem in a very easy and step by step proof.