Final answer:
The sum of the first 6 terms of the geometric series with a first term of 1/2 and a common ratio of 1/2 is 63/128.
Step-by-step explanation:
A geometric series is a series in which each term is found by multiplying the previous term by a constant ratio. The formula for the nth term of a geometric series is given by:
an = a1 * r^(n-1)
Where an is the nth term, a1 is the first term, r is the common ratio, and n is the number of terms.
In this case, a1 = 1/2 and r = 1/2.
To find the sum of the first 6 terms, we can use the formula for the partial sum of a geometric series:
Sn = a1 * (1 - r^n) / (1 - r)
Substituting the given values:
S6 = (1/2) * (1 - (1/2)^6) / (1 - 1/2)
Simplifying the expression:
S6 = (1/2) * (1 - 1/64) / (1/2)
S6 = (1/2) * (63/64) / (1/2)
S6 = (63/128)
So therefore the sum is 63/128.