Question

What is the sum of the infinite geometric series? Sigma-Summation Underscript n = 1 Overscript 3 EndScripts (1.3) (.8) Superscript n minus 1

Answer 1

Answer:

6.5

Step-by-step explanation:

Given the sum of the series represented as $\sum\left {3} \atop {1}} \right (1.3)(0.8)^{n-1}$. To get the sum to infinity of the geometric series, we need to get its first term and its common ratio. comparing to the general term of the sum of series of a GP $\sum\left {n} \atop {1}} \right (a)(r)^{n-1}$

a = first term of the series

r = common ratio

On comparing to the given series, a = 1.3 and r = 0.8

Sum to infinity of a Geometric series is expressed as:

$S_ \infty =\frac{a}{1-r}\\ S_ \infty =\frac{1.3}{1-0.8}\\S_ \infty =\frac{1.3}{0.2}\\S_ \infty = 6.5$