00:01
Let's find the value of c that makes this series equal to 2.
00:06
So this series here, let's rewrite this, because it's actually geometric.
00:19
We can write this as 1 over 1 plus c to the end, geometric, and then r equals 1 over 1 plus c.
00:35
See and we should eventually make sure that the absolute value of r which is absolute value 1 over 1 plus c that this is less than 1 so we have 1 over 1 plus c and absolute value less than 1 that means 1 plus c in the absolute value is bigger than 1 and this tells us that we want 1 plus c bigger than one or one plus c less than minus one.
01:19
So we either want c to be bigger than zero or over here, c less than negative two.
01:28
So we might get more than one answer, but it has to satisfy one of these two.
01:36
So let's keep that in mind.
01:38
C has to be bigger than zero.
01:41
And the reason we want to keep this in mind is in case we have more than one solution.
01:46
Or even if we have one solution, if it doesn't satisfy one of these two.
01:52
For example, c equals negative 1 would not be a good choice.
01:56
It doesn't satisfy one of these two.
02:00
So now, assuming c is bigger than 0 or c less than negative 2.
02:12
So this is just to ensure that the absolute value of r is less than 1.
02:17
We know that the geometric series, we have a formula for this...