Find the sum of the geometric series 1+1/2+1/4+1/8+.....to 12th terms.
S12 = 1(1-(1/2)^12)/(1-(1/2))
To find the sum of a geometric series, you can use the formula:
Sn = a * (1 - r^n) / (1 - r),
where:
- Sn is the sum of the series,
- a is the first term of the series,
- r is the common ratio of the series, and
- n is the number of terms in the series.
In your case, the first term (a) is 1, and the common ratio (r) is 1/2. We are asked to find the sum of the series up to the 12th term (n = 12).
Using the formula, we substitute the given values:
Sn = 1 * (1 - (1/2)^12) / (1 - 1/2).
Now, we simplify the expression:
Sn = 1 * (1 - 1/4096) / (1/2),
Sn = (1 - 1/4096) / (1/2),
Sn = (4096 - 1) / 2,
Sn = 4095 / 2.
Therefore, the sum of the given geometric series up to the 12th term is 4095/2.