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
To compare the two sums and determine which one is larger, we need to evaluate the terms and add them up. Let's break down the steps:
1. Start with the first sum: 7 over Sigma 15/4(pi/10)^n.
- We have a sigma symbol (∑), which indicates that we need to evaluate a sum. In this case, we will be plugging in different values of n into the expression that follows.
- To find the value for each term, we substitute n into the given expression: 15/4(pi/10)^n. For example, if n = 0, the term becomes 15/4(pi/10)^0 = 15/4.
- Then, we add up all the terms by evaluating the expression for different values of n. For instance, if we evaluate the expression for n = 0, 1, 2, and so on, we get a series of terms.
- Finally, we multiply each term by 7 and sum them up.
- This will give us the total value of the first sum.
2. Follow the same steps for the second sum: 11 over Sigma 17/4(4/13)^n.
- Substitute various values of n into the expression 17/4(4/13)^n to get the corresponding terms.
- Multiply each term by 11 and sum them up to obtain the total value of the second sum.
3. Compare the total values of the two sums.
- If the sum obtained in step 1 is larger than the sum obtained in step 2, the first sum is larger by the difference between the two sums.
- If the sum obtained in step 2 is larger than the sum obtained in step 1, the second sum is larger by the difference between the two sums.
- If the two sums are equal, they have the same value.
By following these steps, you should be able to determine which of the two given sums is larger and by how much.