The population of a local species of dragonfly can be found using an infinite geometric series where a1 = 30 and the common ratio is two fifths. write the sum in sigma notation and calculate the sum that will be the upper limit of this population.

The answer is the summation of 30 times two fifth of the i minus 1 power from equation equals to 1, the sum is 50.

Explanation:

S = a ÷ (1-r)

S = 30 ÷ (1- (2÷5))

S = 50.

The sum is 50.

By sigma notation verifies 30.

Step-by-step explanation:

y = a * x(x - 3)(x + 1)^2

2,12 is used to find the value of a

y = a (2)(2 - 3)(2 + 1)^2

12 = a (2)(-1)(3)^2

12 = a (2) (-1) (9)

12 = - 18*a

12/-18 = a

a = - 2/3

y = (-2/3)*x*(x - 3)(x + 1)^2