infinity series??

Question

Find the sums of the following infinite series. Write your answer as a reduced fraction: 0.16 + 0.16^2 + 0.16^3 + ...

 

 

 

Find the sums of the following infinite series. Write your answer as a reduced fraction: 0.58 + 0.58^2 + 0.58^3 + ...

 

 

 

Find the sums of the following infinite series. Write your answer as a reduced fraction: 0.76 + 0.76^2 + 0.76^3 + ...

 

 

 

 

Find the sums of the following infinite series. Write your answer as a reduced fraction: 0.55 + 0.55^2 + 0.55^3 + ...

 

 

 

 

Find the sum of the following infinite series. Write your answer as a reduced fraction: 0.46 + 0.0046 + 0.000046 + ...

 

 

 

 

Find the sum of the following infinite series. Write your answer as a reduced fraction: 0.64 + 0.0064 + 0.000064 + ...

 

 

 

Find the sums of the following infinite series. Write your answer as a reduced fraction: 1 + 0.36 + 0.36^2 + 0.36^3 + ...

 

 

Answer 1

The first one shall be presented as a model. You do the rest in the same manner.

 

S = a / (1 - r), where a = first term, r = common ratio.

 

S = 0.16 / (1 - 0.16)

S = 0.16 / 0.84

S = 4/21

 

The infinite sum of the series is 4/21.