00:01
So in this question, we're going to have a geometric series, and it appears that geometric series is the sum from n equals 1 to infinity of 12 times the quantity of 0 .73 being raised to the n minus first power.
00:22
And we want to know if this geometric series is convergent or divergent.
00:27
If it's convergent, we're going to find its sum.
00:30
So let's start by writing out the terms of this series.
00:36
So when n is 1, my first term is 12 times 0 .73 to the 0 power.
00:46
I get my first term by plugging 1 in for n.
00:51
I get my next term by plugging 2 in for n.
00:56
So that's 12 times 0 .73 to the first.
01:04
And then i plug three in for in.
01:07
So 12 times 0 .73 squared, et cetera.
01:15
Now, this first term, anything to the zero power is 1.
01:18
And so what i'm really getting for this first term is 12 plus 12 times 0 .73.
01:28
There's my second term, plus 12 times 0 .73 squared, plus 12 times 0 .73 squared, plus 12 times.
01:39
0 .73 cubed plus dot dot dot...