infinity series?? each one is hard for me :(

Question

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 formula for the sum of an infinite geometric series is:

 

 

Sum =   a₁ / ( 1 - r)         where a₁  is the first term and r is the common ratio.  Of course r must be less than 1 for this to converge.

 

For the first series    a₁ = 0.58     and r  = 0.58  .  The sum is  .58/(1- .58) =  .58 / .42 =  .29/.21 =  29 /21 .

Since  29 is a prime number, this expression is in lowest terms.

 

The other can be be worked in similar fashion.