Find the indicated partial sum of the series.
infinity
E 3(1/2)^i
i=1
third partial sum
To find the third partial sum of the series, you will need to calculate the sum of the first three terms.
The given series is:
3(1/2)^1 + 3(1/2)^2 + 3(1/2)^3 + ...
To find the third partial sum, you need to sum the first three terms:
S3 = 3(1/2)^1 + 3(1/2)^2 + 3(1/2)^3
Let's calculate it step by step:
1. Evaluate the terms:
The first term is 3(1/2)^1 = 3/2.
The second term is 3(1/2)^2 = 3/4.
The third term is 3(1/2)^3 = 3/8.
2. Add the evaluated terms:
S3 = (3/2) + (3/4) + (3/8)
To add these fractions, we need a common denominator. In this case, the smallest common denominator is 8. Rewrite the fractions with the common denominator:
S3 = (12/8) + (6/8) + (3/8)
3. Add the fractions:
S3 = (12/8) + (6/8) + (3/8) = 21/8
So, the third partial sum of the given series is 21/8.