00:01
In this problem, first let us take the condition that the artist is creating triangles starting from the using the number of tiles as even.
00:13
So we take n as 2m and the tiles would be arranged something like this.
00:21
This is still 2m.
00:23
Next we are subtracting 2, so this is 2m minus 2 and so on.
00:30
We will go on until we finally get 2.
00:34
So the number of tiles will be 2m plus 2m minus 2 plus 2m minus 4 until 2.
00:44
Or this is nothing but taking 2 common summation k equals to 1 to m times k.
00:53
Or this is 2 into m, m plus 1 by 2.
00:57
This is simply m into m plus 1.
01:00
Now m is nothing but n by 2.
01:05
So this becomes n square plus 2m by 4.
01:10
Next case, if it is odd, so it will have the form 2m plus 1...