The population of a local species of bees can be found using an infinite geometric series where a1=860 and the common ratio is 1/5. write the sum in stigma notation and calculate the sum that will be the upper limit of this population

Answer: 1,075explanation: a geometric series means that each term is equal to the previous terms times the common ratio.this is aₓ = aₓ₋₁ rgiven a₁ = 860 and r = (1/5) you have: a₁ = 860a₂ = 860 (1/5)¹a₃ = 860 (1/5)²a₄ = 860(1/5)³a₅ = 860(1/5)⁴  aₓ = 860(1/5)ˣ⁻¹and the sum of the terms is:     ∞    ∑ (860)(1/5)ⁿ⁻¹ = 1,075.n = 1for that you can use the formula for the sum of an ininite series (when |r| < 1) :   ∞    ∑ arⁿ = a  / (1 - r) n = 1therefore, with a = a₁ = 860, and r = 1/5  ∞    ∑ (860)(1/5)ⁿ⁻¹ = 860 / [ (1 - (1/5) ] = 860 / (4/5) = 860× 5 / 4 = 1,075.n = 1that is the answer: 1,075.

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