Find the sum to infinity of the geometric progression with the first 3 terms 0.5, 0.125, 0.03125

Question

Find the sum to infinity of the geometric progression with the first 3  terms 0.5, 0.125, 0.03125

anonymous · Answer

can you tell what is the common ratio r here?

anonymous · Answer

Hint: Common ratio r is the ratio of two successive terms in GP..
$$r=\frac{ x _{n+1} }{ x }$$

anonymous · Answer

common ratio = 0.25..?

wolf1728 · Answer

It seems to me that the series is based on this formula:
1/(2^n)

So the first 3 numbers are:
1/2^1
1/2^3
1/2^5

anonymous · Answer

$$S=\lim_{n \rightarrow \infty}\frac{ a_1-a_{n+1} }{ 1-r }$$

anonymous · Answer

$$a_1=0.5$$$$\lim_{n \rightarrow \infty}a_{n+1}=0$$$$r=0.25$$ and$$S=\frac{ a_1 }{ 1-r}$$

anonymous · Answer

Simply use the formula that CarlosGP mentioned i.e 

S= a/ (1-r) 
    where a= first term |
              r= common ratio 

S= 0.5/ (1-0.25) = ?