Question 483711

In a geometric series, finite or infinite, the {{{common}}} {{{ratio}}} is the multiplier used to get each succeeding term.  Or, you can think of it as any term divided by the previous one.  

For example, in the series you have


1.1+0.11+0.011+.............the common ratio is {{{0.1}}} 

If an infinite geometric series has a ratio whose absolute value is less than {{{1}}}, and so has a {{{sum}}}, the formula is

             {{{S(inf) = a / (1-r)}}}  

 where {{{S(inf)}}} just stands for the sum of an infinite series,{{{ a}}} is the first term, and {{{r}}} is the common ratio.

in your case:

 {{{S(inf) = 1.1 / (1-0.1)}}} 

 {{{S(inf) = 1.1 / (0.9)}}} 

{{{S(inf) = 1.2222222222222222222222222222222}}} 


{{{S(inf) = 1.2}}}