 I am going to help you to solve the following question. The question says show that the ratio of the sum of first N terms of a GP to the sum of terms from N plus 1F to 2NF term is 1 by RN. Let's now begin with the solution. Let A be the first term, R be the common ratio of the given GP. N terms of GP is equal to AR plus AR square plus so on plus AR to the power N minus 1. Now you know that sum of N terms of GP is equal to A into 1 minus R to the power N upon 1 minus R if R is less than 1. Now N plus 1F term that is TN plus 1 is equal to A into R to the power N. N plus 2 is term that is TN plus 2 is equal to A into R to the power N plus 1 and 2NX term that is T2N is equal to A into R to the power 2N minus 1. Now sum of terms plus 1F to 2NF terms is equal to N plus 1 plus EN plus 2 plus so on till 2NF term that is T2N. Now this is equal to A into R to the power N plus A into R to the power N plus 1 plus so on till A into R to the power 2N minus 1. Now we will find the sum of these terms. Now here the first term is A into R to the power N. So the sum of these terms is A into R to the power N into 1 minus R to the power N upon 1 minus R. Let's name this equation as equation number 2 and this equation as equation number 1. Now dividing 1 by 2 we get sum of first N terms of GP upon sum of 2 plus 1F is equal to 1 minus R to the power N upon 1 minus R divided by A into R to the power N into 1 minus R to the power N upon 1 minus R. Now this is equal to 1 by R to the power N. We have proved that 2 of sum of first N terms of GP to the sum of terms from N plus 1F to 2NF term is 1 by R to the power N. This completes the session. Bye and take care.