00:02
I want to find out here the last digit of this, last digit of this expression and evolve this here.
00:10
So let's first find out the last digit here.
00:12
So understand the method here, how to find the last digit for any given series.
00:19
So here we have let's put 3 to the bar 100.
00:22
Take here 3 to the par 100.
00:27
Now what we can do, we can just bring out 3 in terms of 10.
00:32
Or if find out here for let's say 17 to the power 50 we can bring out 17 in terms of 10 a multiples of 10 that's what we can do here so if we have three now three we just bring in multiples of 10 and other number is one what you can do here you can just use like this so we have three square to the power 50 will be 10 negative 1 to the power 50.
01:05
So here we go to our series here.
01:08
10 negative 1 to the power 50, that we can expand easily.
01:12
So now, let's expand it out.
01:14
So we get here, it's coming out to be 50, p 0, then we have 10 to the power 50 plus 50, 10 to the power 49, negative 1 to the power 1, and so on.
01:33
Last time it's coming out to be negative 1 to the power 50, we'll have negative 1.
01:40
The part 50.
01:43
So now see here, this is here, it is coming out to be one.
01:52
This part is one.
01:54
This is even number, this is even number.
01:56
This part is one.
01:57
Let's look at here from 50c 0, 501, 5049.
02:02
Let me analyze that.
02:03
That's coming out to be a multiple of 10.
02:06
That's coming out to a multiple of 10 here and so on.
02:10
So from 50c 0 to 50c 49.
02:14
If we get it as let's say 10m and then plus one for the last term.
02:21
Where m belongs to natural number, so m belongs to a natural number.
02:25
So because we just need the last digit.
02:27
So now the last digit for this will be 0 plus 1.
02:31
So the last digit is coming out to be 1.
02:37
Next the same method we applied here to find out the last digit 4.
02:40
17 to the part 50, 17 to the part 50.
02:44
So we can write that 17 square.
02:47
To the part 25, there'll be 289, it'll be 290, negative 1.
02:53
So we go to a multiple of 10 here, and then negative 1, to the part 25.
03:01
So if you go all this now, by same method here, what you've done here, so we get it as 10 and negative 1, where m belongs to a natural number.
03:13
So for this number, the last digit will be 0...