The infinite sum, ----- equals
This is a simple example of a series called Arithmetic-Geometric Progression.
Let the sum that you need to find be S.
(eqn 1)
Multiply S by the common ratio (in this case 1/7 )
So, we get,
.. (eqn 2)
Subtract equation 2 from 1,
We now see that the numerators on the right hand side form an arithmetic progression. For solving this type of a problem, multiply both sides by the common ratio again ( 1/7 ) and subtract.
The terms in the bracket form a simple infinite geometric progression.
(Refer Geometric progression if you are unaware of the formula)
S(36/49)=1+2[(1/7)/(1−1/7)]
S(36/49)=4/3
S=49/27