Hello students, myself Dr. Gajendra Purohit and I
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Hello students, myself Dr. Gajendra Purohit
and today i will start
alternating series and what is alternating series and how
we use a test for this series
and normally we use a leibniz test for this series and
after this series there is another concept of absolute convergence
and conditional convergence and for these concepts
i will bring my next video for you all on this topic. So students
before this all my videos that I have uploaded on infinite series
in which I have uploaded different tests
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so students what is alternating series
can you can see from the name that here alternating negative positive will come
but the main definition for this will be
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
so these types of series are known as
alternating series. now these alternating series
now students how to find
that these series are convergent or not .Right
so for that leibniz gave test and leibniz
told that for a series
i will tell you a definition for that
but this is a decreasing type of series
this term is smaller than that term
plus the n term
for n tends to infinite the term becomes 0
then that series is the convergent series and that i will tell you with the definition
and i will explain what is leibniz test and we will discuss
with examples. So i will tell you more about it
so students see this question here
first i will tell you what is leibniz test and how
we find convergent and divergent for an alternating series
so students here leibniz gave a test
leibniz test for the convergence of an alternating series
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
so like this we use this test
to find if the series is convergent or not
so i will take one or two more questions and then we will finish this topic
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
so students see this last question on leibniz test
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
so if you face any problem you can go to this I icon
and see the D'Alembert's ratio test  and you will understand that
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
so these types of questions can also come in the exam
in this question
this question is important  because in this we are applying D'Alembert's ratio test and then leibniz test
concept is also applied. we are checking on all different conditions
so students these types of questions are important so in my next video
i will take the topic on absolute convergence
and conditional convergence concept and how to solve questions on them
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