Final answer:
To evaluate the series, we can use the formula for the sum of a geometric series. In this case, the sum is -174762.
Step-by-step explanation:
To evaluate the series ⁹Σₖ_=₁ 2(4)ᵏ⁻¹, we can use the formula for the sum of a geometric series. When the first term is a and the common ratio is r, the sum of the series is given by:
S = a(1 - rⁿ) / (1 - r)
In this case, the first term is 2(4)⁰ = 2 and the common ratio is 4. The number of terms in the series is 9. Plugging these values into the formula, we get:
S = 2(1 - 4⁹) / (1 - 4) = 2(1 - 262144) / -3 = 524286 / -3 = -174762.