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20 July, 09:37

The population of a local species of dragonfly can be found using an infinite geometric series where a1=30 and the common ratio is 2/5. write the sum in sigma notation and calculate the sum that will be the upper limit of this population.

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  1. 20 July, 12:22
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    The sum of any geometric sequence (if it converges, r^2<1) is of the form:

    s (n) = a (1-r^n) / (1-r), a=initial term, r=common ratio, n=number of terms ...

    s (n) = 30 (1-0.4^n) / (0.6)

    s (n) = 50 (1-0.4^n)

    Since r<1 the sum of the infinite series is just:

    s=50
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