I will show you this example so you can have a template to do others. OK?.
Mark off your decimals places by separating the 45's. At each 45, replace the numbers in front with 0's so you can keep track and see the pattern. See what I mean?.
Removing the 1.7, we have .0454545..........
Then, there are 3 decimal places to the next 45, .00045
And so on. See?.
From the beginning, we have 1+(7/10)=1.7. OK so far?.
Then, we have .045+.00045+.0000045+....................
The first term is \(\displaystyle a=\frac{9}{200}=.045\)
Subsequent terms follow \(\displaystyle \frac{1}{100^{k}}\)
So, we have a geometric series with first term a=9/200 and common ratio r=1/100.
Using the formula \(\displaystyle \frac{a}{1-r}\)
\(\displaystyle \frac{9}{200}\sum_{k=1}^{\infty}\frac{1}{100^{k}}=\frac{\frac{9}{200}}{1-\frac{1}{100}}=\frac{1}{22}=.0454545.............\)
Add them up: \(\displaystyle 1+\frac{7}{10}+\frac{1}{22}=\frac{96}{55}=1.7454545.......................\)
