Question

Help please? :) Find the sum of the infinite geometric series 5 + 5/3 +5/9 +5/27+... if it exists

Answer 1

it's a infinite gp series.

Answer 2

\[\large \sum_{n=1}^{\infty}5(\frac{1}{3})^{n-1}\]I beleive.

Answer 3

So utilizing definition, \(\ |r|<1\).

in our case, \(\large r = \frac{1}{3}\) sO we have found that it converges.

Then we use our sum, \(\large \frac{a}{1-r}\) \[\large a= 5 \ , \ r = \frac{1}{3}\]\[\large \frac{5}{1-\frac{1}{3}} = \frac{5}{2/3} = \frac{5 \cdot 3}{2} = ?\]