00:01
In this question, we are asked to approximate the sum of the given series to 4 decimal place accuracy.
00:08
And this means that we want the absolute value of s minus s n capital to be less than 10 to the negative 4th power.
00:18
Where s is the sum of the series and s n capital is the nth partial sum and equals to the sum of the first n capital terms of the series.
00:29
And we want their difference to be less than 10 to the negative fourth power.
00:42
And by the alternating series remainder estimation theorem, this difference is lessen a and capital plus 1, where a .n equals to the absolute value of the general term of the series equals to 1 over n to the fuse power.
01:07
Therefore, a .n plus 1 equals to 1 over and plus 1 to the 5th power.
01:13
And since we want this difference to be less than 10 to the negative 4th power, we want a .n plus 1 to be less than 10 to the negative 4th power.
01:23
So we want to find the value of n capital for which this inequality is true.
01:31
So the inequality is 1 over n capital plus 1 to the 5th power less than 1 over 10 to the 4th power, right? because 10 to the negative 4 is 1 over 10 to the 4.
01:46
And this equals to 1 over 10 ,000.
01:52
What we are going to do now is just start plugging in different values of n.
01:57
We will start with n equals 1.
01:59
For n equals 1, we are going to get 1 over 1 plus 1 to the 5th power equals to 1 or 2 to the 5 equals to 1 over 32, well, which is clearly greater than 10 to the negative 4.
02:18
So this doesn't work...