00:01
In this question, for the series below, we're going to calculate the sum of the first four terms, s4, and we're going to find it bound for the error.
00:07
We're going to make sure that we include several decimals for accuracy when the problem is graded.
00:13
So here i'm looking at the sum from n equals 1 to infinity of negative 1 to the n times 400 over n to the power of 0 .9.
00:23
So if i want s4, the sum of the first four terms, first when n is 1.
00:31
I have negative 1 to the first power.
00:34
That's negative 1 times 400.
00:38
Negative 400 over 1 raised to the 0 .9 power, that's just 1.
00:45
Then when n is 2, i've got negative 1 squared.
00:49
That's a positive 400 over, we're going to have 2 raised to the power of 0 .9.
01:01
Then when n is 3, negative 1 cubed is negative 1, 400 over 3 to the power of 0 .9.
01:13
And then when n is 4, i get negative 1 to the fourth, which is a positive 400 over 4 to the power of 0 .9.
01:24
And so i'm going to head to my calculator and i'm going to say, okay, i've got negative 400 over 1, and then it's plus 400 over 2 to the power of 0 .9...