Question

Evaluate the series 9 + 3 + 1 +

Answer 1

Answer:

9 + 3 + 1 + ......... = 13.5

Step-by-step explanation:

The series 9 + 3 + 1 +  is the sum of an infinite geometric sequence. The first term of the series is 9 while the common ratio is 1/3;

to obtain the common ratio we obtain the quotient of any two successive terms, 3/9 or 1/3.

The sum of an infinite geometric series with first term a and common ratio r is given by;

$S_{n}=\frac{a}{1-r}$

Plug in the values of a and r into the formula;

$S_{n}=\frac{9}{1-\frac{1}{3} }\\\\\\S_{n}=\frac{27}{2}=13.5$