Question 1066079
If  |r| < 1 then {{{ sum(a*r^n)  = a/(1-r) }}} 

We have  a=75/100
               r = 1/100

        {{{sum((75/100)*(1/100)^n) = (75/100)/(1-(1/100)) = (75/100)/(99/100) = 75/99 }}}

—
Answer is  {{{highlight(75/99)}}}

—
Check:  One way is to just divide 75/99 to see it gives you 0.75757575…

Another way is as follows (this works on any decimal that repeats):
                       Let       n = 0.75757575….
                             100n = 75.757575...
                        Subtract top from bottom (all numbers to the right of decimal cancel):
                              99n = 75  —>   n=75/99