determine the sum of:
50 over Σ 8(.5)^n-2
n=1
To determine the sum of the given series, we need to evaluate each term of the series and then add them together.
The series is represented as:
Σ 8(.5)^(n-2)
Let's break it down step by step:
1. Start with the first term, where n = 1:
- Plug in n = 1 into the series, we have: 8(.5)^(1-2) = 8*(.5)^(-1) = 8*(1/2) = 4
2. Move on to the second term, where n = 2:
- Plug in n = 2: 8(.5)^(2-2) = 8*(.5)^0 = 8*1 = 8
3. Continue this process for each consecutive term by incrementing the value of n:
- n = 3: 8(.5)^(3-2) = 8*(.5)^1 = 8*(1/2) = 4
- n = 4: 8(.5)^(4-2) = 8*(.5)^2 = 8*(1/4) = 2
- n = 5: 8(.5)^(5-2) = 8*(.5)^3 = 8*(1/8) = 1
4. Add up all the terms obtained in steps 1-3:
- 4 + 8 + 4 + 2 + 1 = 19
Therefore, the sum of the series Σ 8(.5)^(n-2) where n=1 is 19.