the number 0.3 can be written 0.3+0.03+0.003+0.0003, find the value of s, of the convergent infinite series using the formula s=a1/1-r

Question

math help

 

Answer 1

I am not sure I completely understand your question. I will try anyway.

 

to express the repeating decimal 0.3333333... as the sum of an infinite geometric series, set a = 0.3 = 3/10 and r = 0.1. The first term will be multiplied repeatedly by 0.1 to obtain the other terms:

 

a = 0.3,

ar = 0.3 · 0.1 = 0.03

ar² = 0.3 · (0.1)² = 0.003

ar³ = 0.3 · (0.1)³ = 0.0003

 

The sum is, therefore, s = a(1 - r) = 0.3/(1 - 0.1) = 0.3/0.9 = 1/3.

 

But you already knew that, didn't you.