Answer:
For the 7th term we have 3 decimals of approximation but our value is 0.000198 higher than the error required, so we can use the 8th term and we have that 
and with this we have 4 decimals of approximation so if we add the first 8 terms we have a good approximation for the series with an error bound lower than 0.0001.
Step-by-step explanation:
Assuming the following series:
We want to approximate the value for the series with less than 0.0001 of error.
First we need to ensure that the series converges. If we have a series 
where 
[/tex] or 
where 
for all n if we satisfy the two conditions given:
1) 
2) {
} is a decreasing sequence
Then is convergent. For this case we have that:
And 
because 
and 
So then we satisfy both conditions and then the series converges. Now in order to find the approximation with the error required we can write the first terms for the series like this:
For the 7th term we have 3 decimals of approximation but our value is 0.000198 higher than the error required, so we can use the 8th term and we have that and with this we have 4 decimals of approximation so if we add the first 8 terms we have a good approximation for the series with an error bound lower than 0.0001.
Associative property!
The property states that when three or more numbers are added (or multiplied), the sum (or the product) is the same regardless of the grouping of the addends!
Hope this helps!
There are an infinite number of answers. One possible answer is 3.5+1.2+2.4+3.9=11. The explanation of how I arrived at this follows: A mixed decimal is a whole number followed by a fractional part so an example would be 3.4 or 2.5. To get 4 different mixed decimals that sum to 11 follow these steps: 1. Start with 11 and subtract any mixed decimal from 11 that is smaller than 11. So I will subtract 3.5 11-3.5=7.52. Take the 7.5 from the last step and subtract another mixed decimal from 7.5 that is smaller than 7.5. I will subtract 1.2 7.5-1.2=6.33. Take the 6.3 and subtract another mixed decimal from 6.3 that is smaller than 6.3. I will subtract 2.4 6.3-2.4=3.94. Now I take all of the numbers that I subtracted and add them together along with the 3.9 that was left over and I get 3.5+1.2+2.4+3.9=11
I hope that this helps you! =D
