Answer:
[tex]\frac{40}{27}[/tex]
Step-by-step explanation:
We need to evaluate the sum of the following finite geometric series.
We need to define r and [tex]a_{n}[/tex]
[tex]r = 1/3[/tex]
[tex]a_{n} =(\frac{1}{3} )^{n-1}[/tex]
Follow the geometric sequence sum formula and substitute :
[tex]1*\frac{1-(\frac{1}{3})^4 }{1-\frac{1}{3} }[/tex]
Simplify :
[tex]1 * \frac{3*\frac{80}{81} }{2}[/tex]
Get rid of the 1 :
[tex]\frac{3*\frac{80}{81} }{2}[/tex]
Multiply the numerators :
[tex]\frac{\frac{80}{27} }{2}[/tex]
Move the denominator of the fraction in the numerator and move it to the denominator of the whole fraction :
[tex]\frac{80}{27*2}[/tex]
Multiply the denominators :
[tex]\frac{80}{54}[/tex]
Simplify by dividing both the numerator and denominator by 2 :
[tex]\frac{40}{27}[/tex]
