Question

Which of the following represents the series in summation notation?

Answer 1

Answer with explanation:

The given series is:

    $\Rightarrow 3+\frac{3}{5}+\frac{3}{25}+\frac{3}{125}+\frac{3}{625}+.........\\\\\Rightarrow 3+\frac{3}{5}+\frac{3}{5^2}+\frac{3}{5^3}+\frac{3}{5^4}+.........$

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 $=\frac{\frac{3}{5}}{3}\\\\=\frac{1}{5}$

In Summation Notation

   $\sum_{k=1}^{k=\infty} \frac{3}{5^{k-1}}$

Answer 2

$\sum_{n=0}^{4} \frac{3}{ {5}^{n} }$