which of the following sums is larger and by how much?
1. 7 over Sigma 15/4(pi/10)^n
2. 11 over Sigma 17/4(4/13)^n
please help me with the steps on how to figure this out! thanks
did you mean
Σ ((15/4) (π/10)^n , where n goes from 1 to 7 ?
of so, then you would have
(15/4) [ π/10 + π^2/100 + ... + π^7/10^7)
the [..] is a geometric series where a=π/10 and r = π/10 for 7 terms
the value of the [..]
= (π/10)((π/10)^7 - 1)/(π/10 - 1) = appr. .4579
so
Σ ((15/4) (π/10)^n , where n goes from 1 to 7
= (15/4)(.4579) = 1.717
evaluate the second part the same way, and compare sums
I believe the answer was IF so not OF so, thank you.
To compare the sums given in the question, we need to find the values of both sums and determine which one is larger and by how much. Let's go step by step:
1. Let's start with the first sum: 7 over the sigma of (15/4)(pi/10)^n.
To calculate this sum, we need to find the values of the terms in the sum and add them up.
- Start by substituting n = 0 into the expression (15/4)(pi/10)^n:
(15/4)(pi/10)^0 = (15/4)(1) = 15/4
- Substitute n = 1 into the expression:
(15/4)(pi/10)^1 = (15/4)(pi/10)
- Next, substitute n = 2:
(15/4)(pi/10)^2 = (15/4)(pi/100)
- Continue the process for a few more values of n, if needed, until you can see a pattern emerging.
Once you have the values of the terms for a few consecutive values of n and have identified the pattern, you can generalize it. This will allow you to describe the sum without having to calculate each term individually.
2. Now let's move on to the second sum: 11 over the sigma of (17/4)(4/13)^n.
Just like before, we need to find the values of the terms and add them up to get the sum.
- Substitute n = 0 into the expression to find the first term:
(17/4)(4/13)^0 = (17/4)(1) = 17/4
- Substitute n = 1:
(17/4)(4/13)^1 = (17/4)(4/13)
- Continue this process to find the pattern and generalize it for the sum.
3. Once you have the general forms of both sums based on the patterns you identified, compare them to determine which one is larger. You can do this by comparing the leading coefficients or by inspecting the exponents and the base values.
4. Finally, if one sum is larger than the other, subtract the smaller sum from the larger sum to find the difference between the two sums.
By following these steps, you can find which of the given sums is larger and by how much.