Question

Which of the following represents the series in summation notation?

3 + 3/5 + 3/25 + 3/125 + 3/625

Answer 1

`\sum_(n=0)^(4) \frac{3}{ {5}^(n) }`

Answer 2

Answer with explanation:

The given series is:

`\Rightarrow 3+(3)/(5)+(3)/(25)+(3)/(125)+(3)/(625)+.........\\\\\Rightarrow 3+(3)/(5)+(3)/(5^2)+(3)/(5^3)+(3)/(5^4)+.........`

This is a Geometric Expression because the ratio of next term to Previous term is Constant for any two consecutive term in the series which is equal to
`=((3)/(5))/(3)\\\\=(1)/(5)`

In Summation Notation

`\sum_(k=1)^(k=\infty) (3)/(5^(k-1))`