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Identify whether the series summation of 8 open parentheses 5 over 6 close parentheses to the I minus 1 power from 1 to infinity is a convergent or divergent geometric series and find the sum, if possible.

a.This is a convergent geometric series. The sum is 48.

b.This is a divergent geometric series. The sum is 48.

c.This is a convergent geometric series. The sum cannot be found.

d.This is a divergent geometric series. The sum cannot be found.

Answer :

nobillionaireNobley
Summation from i = 1 to infinity of 8(5/6)^(i - 1)

Because 5/6 is less than 1, the series is convergent.

The series is given by 8(5/6)^0 + 8(5/6)^1 + 8(5/6)^2 + . . . to infinity
Sum of G.P. to infinity is a/(1 - r) = 8/(1 - 5/6) = 8 / (1/6) = 8 * 6 = 48.

Therefore, option a is the correct answer.

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