# 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

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