Where all do we apply like this...why we have used this method putting all 2 power n

convergent

Do you get it?

I suggest you to see first check if series is geometric and if yes then then apply geometric test and if not then go for other test.Or when they ask about exact sum of series then ...

Because if series is geometric then we are able to find sum also whereas other tests just tell us about convergence and divergence but not exactly sum.

then why do we use geometric series to get the answer

Madhu you should not get confused with geometric test and ratio test. sometimes ratio test can be applied to questions whereas geometric can't.

Whenever there is a polynomial or factorial then this ratio test should be apply until it get failed. Whenever exponential type of coefficients then apply nth root test

option a. see attachment