Question

Identify whether the series summation of 12 open parentheses 3 over 5 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.

Answer 1

∑ from 1 to infinity of 12(3/5)^(i - 1)
Since the common ratio is less than 1, the series is convegent. [i.e. 3/5 < 1]

Sum to infinity of a geometric series is given by a/(1 - r); where a is the first term, and r is the common ratio.

Sum = 12/(1 - 3/5) = 12/(2/5) = 30.