What is the sum of the infinite geometric series? Sigma-Summation Underscript n = 1 Overscript 4 EndScripts (negative 144) (one-half) Superscript n minus 1

Step-by-step explanation:

∑⁴ₙ₌₁ - 144 (½) ⁿ⁻¹

This is a finite geometric series with n = 4, a₁ = - 144, and r = ½.

S = a₁ (1 - rⁿ) / (1 - r)

S = - 144 (1 - (½) ⁴) / (1 - ½)

S = - 270

If you wanted to find the infinite sum (n = ∞):

S = a₁ / (1 - r)

S = - 144 / (1 - ½)

S = - 288

The answer is C (40)