Step-by-step explanation:
1) repeated Infinite decimals are geometric sequences.
x= 0.045 + 0.045*0.01 + 0.0045*0.01^2 and so on.
Convert it to a function.
[tex]x=0.045(0.01)^n[/tex]
Be Careful!!! this is not the answer.
We found the function that represents the sequence {0.045, 0.00045, 0.0000045...}
Now, because the infinite decimal is the SUM of these terms in the sequence, we have to use summation.
S∞ = a1 / (1-r ) is the summation for infinite geometric sequence.
a1=0.045
r=0.01
S=0.045/(1-0.01)=0.045/0.99=45/990= 1/22
2)
convert 0.136 and 0.2 to fractions (follow the same steps as in #1):
S∞ = a1 / (1-r )
Then multiply the two fractions to get 1/33:
I'm really sorry but I really don't have time to write all these processes
Just follow the steps in #1
Good Luck ;)
