Find the sum of the infinite geometric series whose first term is 4,374 and whose common ratio is -1/3.

1. First check the sum exists: the ratio -1/3 lies strictly between -1 and 1, so it does. 2. The infinite sum formula is S = a_1/(1 - r). 3. The denominator is 1 - (-1/3) = 1 + 1/3 = 4/3. 4. So S = 4,374 divided by 4/3. 5. Dividing by 4/3 is the same as multiplying by 3/4, giving 4,374 times 3/4. 6. That is 13,122/4 = 3,280.5. 7. Dropping the sign and using 1 - 1/3 = 2/3 in the denominator would give 6,561, which is the commonest error with a negative ratio. _Source: OpenStax Algebra and Trigonometry (CC BY 4.0), Ch 13 "Sequences, Probability and Counting Theory", section 13.4 Series and Their Notations_