Answer: 59,048
Explanation:
To find the sum of the given finite series:
Σ2· (3)n-1
n=1
where n ranges from 1 to 10, we can use the formula for the sum of a geometric series.
The formula for the sum of a geometric series is:
S = a * (r^n - 1) / (r - 1)
In this case, a = 2 (the first term of the series) and r = 3 (the common ratio).
Using the formula, we can calculate the sum:
S = 2 * (3^10 - 1) / (3 - 1)
= 2 * (59049 - 1) / 2
= (118098 - 2) / 2
= 118096 / 2
= 59048
Therefore, the sum of the given finite series is 59,048.