Question

Evaluate the series 9 + 3 + 1 +

Answer 1

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

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)=(a)/(1-r)`

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

`S_(n)=(9)/(1-(1)/(3) )\\\\\\S_(n)=(27)/(2)=13.5`