Find the sum :

We can write the above expression as:


The given expression can also be written as


…(1)


Now for the first term is in GP.


…upto 10 terms


Common Ratio = r =


Sum of GP for n terms = …(2)


a = 1, , n = 10


Substituting the above values in (2) we get,





Now for the second term is in GP.


…upto 10 terms


Common Ratio =


Sum of GP for n terms = …(2)


, , n = 10


Substituting the above values in (2) we get




Total sum



12