00:01
Now to determine whether this g1 series which is summation of minus 1 to the power n minus 1 5 to the power n divided by n factorial.
00:14
Whether it is convergent we need to tell whether it is convergent or divergent.
00:24
So, first of all we have to tell which test we are using.
00:28
So, we will use the alternating series test to tell about whether this is convergent or divergent.
00:48
In this series test it states that if we have a series of the form of n equals to 1 to infinity minus 1 to the power n minus 1 an and this is also n equals to 1 to infinity as it shows where this an is a positive and decreasing sequence.
01:21
Now we will see that what is decreasing sequence.
01:29
If it means if an plus 1 is less than or equals to an for all n.
01:40
Now just in this equation we can see because n factorial is in denominator part.
01:48
So, definitely if we will put n equals to 1 so it will give us something divided by 1 factorial n equals to 2 it will give us something divided by 2 factorial n equals to 3 something divided by 3 factorial means the biggest term is this one then this one then this one.
02:09
So, definitely and we can say this is for all n and we can say that if this is n plus 1 so 2 will be if just imagine that n equals to 1 so 2 will be n plus 1...