00:01
In this question, we are asked to determine if the given series converges or diverges by using the comparison test.
00:08
And let's look at the denominator of the series, of the general term of the series.
00:15
3 plus 8n.
00:17
Note that it's less than 8 plus 8n, right? therefore, if we take the reciprocals, we are going to get the reverse inequality.
00:26
1 or 3 plus 8n is greater than 1.
00:31
Over 8 plus 8n.
00:35
Now that we can write 1 over 8 plus 8 n as 1 over 8 times n plus 1.
00:44
And this means that 7n over 3 plus 8 is greater than 7n divided by 8 times n plus 1.
01:00
And if we replace 7n by 1, we are going to get that this is greater than 1 over 8 times n plus 1.
01:11
Now let's look at the series whose general term is 1 over 8 and plus 1.
01:25
Where n is running from 1 to infinity.
01:28
Let's factor out 1 over 8...