Question

HELP, ALG 2 DIVERGENT AND COVERGENT SERIES
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.

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

This is a convergent geometric series. The sum is 30.

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

This is a divergent geometric series. The sum is 30.

Answer 1

@ShadowLegendX PLEASE HELP

Answer 2

Convergent series have sums, and divergent series don't have sums, so you can eliminate the first and last options.

Answer 3

Is the series
\[\large\sum_{i=1}^\infty12\left(\frac{3}{5}\right)^{i-1}~~?\]

Answer 4

If it is... recall that a geometric series with ratio \(r\) converges for \(|r|<1\), or \(-1<r<1\).

Does \(r=\dfrac{3}{5}\) fall between -1 and 1? If yes, the series converges. If no, it diverges.

Answer 5

If you think it converges, you can use this formula to find the sum:
\[\large\sum_{i=1}^\infty ar^{i-1}=\frac{a}{1-r}\]