 Hi and welcome to the session. I am Asha and I am going to help you with the following question which says, a person writes a letter to four of his friends. He asks each one of them to copy the letter and mail to four different persons with instructions that remove the chain similarly assuming that the chain is not broken and that it costs 50 paisa to mail one letter, find the amount spent on the postage when eight set of letters is mailed. To start with the solution, a person writes a mail to persons and he asks each person to write the same mail four times and send it to four different persons again. So again he sends to four different persons, he again sends to four different persons, third one also and the fourth one also. So first the number of letters posted were four and in the second chain the number of letters posted will be 16. The number of letters posted will form a GP, the number is four then these four persons write four letters each and so send it to sixteen persons. Now sixteen different persons again write four four letters each and so the mail letter to sixty four persons and the GP series goes on like this. Note that small eight is four, the common ratio which is greater than one. So the number of letters posted is equal to into R is again four raised to the power eight minus one upon four minus one since for a GP series A, AR, AR square and so on, sum of n number of terms as A into R raised to the power n minus one if R is greater than one. So this is further equal to four upon three into four raised to the power eight minus one which further implies four upon three inside the bracket four raised to the power eight is equal to four raised to the power four minus one into four raised to the power four plus one A square minus B square is equal to A minus B into A plus B and therefore four raised to the power eight can be written as four raised to the power four whole square. This is further equal to four upon three into two hundred fifty six minus one into two hundred fifty six plus one is equal to four upon three into two fifty five into two fifty seven which implies four upon three into six five five three five which is further equal to eight seven three eight zero postage the rate of fifty paisa per letter is equal to rupees fifty upon hundred into the number of letters posted to eight seven three eight zero so this is equal to rupees five into eight seven three eight which is further equal to rupees four three six nine zero therefore end on postage when the eight set of letter is made is rupees four three six nine zero so this completes the session take care and have a good day