Answer:
The other guy is correct except for question five.
If your question is "Use summation notation to write the series 2+4+6+8+... for 10 terms. In each of these images, the lower limit of the summation notation is either "n=1" or "n=0".
The answer should be 10∑n=1 (2n) not (n+2)
The correct option is (C) it converges it has a sum.
An infinite geometric series is an infinite series whose successive terms have a common ratio. This is easily proven by using an infinite geometric series. This series would have no last term. The general form of the infinite geometric series is[tex]a + a r + a r^ 2 + a r ^3 +...[/tex]+ ..., where [tex]a[/tex] is the first term and [tex]r[/tex] is the common ratio.
We can find the sum of all finite geometric series.
Given series can be written as;
[tex]\frac{1}{5}+\frac{1}{10}+\frac{1}{20}+\frac{1}{40}+..... \\ a=\frac{1}{5} \\ r=\frac{1}{2} \\ \Rightarrow \frac{a}{1-r}=\frac{1/5}{1-1/2} \\[/tex]
[tex]=\frac{2}{5}[/tex]
Therefore, [tex]\frac{2}{5}[/tex] is infinite, so it converges.
Learn more about the topic Infinite Geometric Series: https://brainly.com/question/12213123
