00:01
In this question, we are given that the sum of the series negative 1 to the n, 1 over 8 to the k and plus 2, equals to 1 over 65.
00:09
And we are asked to find the value of k.
00:12
First of all, note that the series on the left side is a geometric series.
00:18
This means we can find the sum of the series.
00:22
However, first we need to find the common ratio and the first term of the series.
00:39
Let's write down the first few terms of the geometric series.
00:43
For n equals 0, we are going to get.
00:45
Get 1 or 8 squared.
00:47
For n equals 1 we're going to get negative 1 over 8 to the k plus 2.
00:55
For n equals 2 we are going to get 1 over 8 to the 2 k plus 2 and so on...