00:01
So the first thing we need to do is we need to calculate the first 10 terms of the sequence.
00:17
And to do that, i will replace n with the number of the term.
00:23
So 3 times 1 over 1 plus 6 times 1.
00:28
So that becomes 3 sevenths.
00:30
Then i'll do it again with a 2, sorry, 6 times 2.
00:38
So that's 6 thirteenths.
00:40
You might see a pattern forming here, especially in the numerator.
00:45
3 sixths.
00:49
The next one's 9.
00:51
9 nineteenths.
00:53
And then i keep going with that substitution and these will be the next answers.
01:01
Again, simply substituting in.
01:04
So i'll do this one again.
01:05
The number that i'm using for n in place of n.
01:12
So this becomes 18 over 37.
01:15
Supposed to be a 49.
01:33
24 over 49.
01:36
27 over 55.
01:38
And finally, 30 over 61.
01:43
So to plot these, it might be a little easier to change all these to decimals in order to plot them.
01:50
So if we change this one to a decimal, it's 0 .428646154737 .48 .4839.
02:11
So even just looking at the decimals, it does appear that it has a limit.
02:20
So let's see...