 Hi, and welcome to the session. Let us discuss the following question. The question says find the sum to n terms of the sequence 888, 888, 888, and so on. Let's now begin with the let s denote the sum in terms of the series 8 plus 88 plus 80088 plus 880088 plus so on. Since s is denoting the sum of n terms of the series 8 plus 88 plus 80088 plus so on, therefore s is equal to 8 plus 88 plus 80088 plus 8888 plus so on. Now we will try to convert this into series into GP. Let's now take 8 common from this, but taking 8 common we get 8 into 1 plus 11 plus 111 plus 1111 plus so on. Now multiply and divide this by 9. So by multiplying and dividing this by 9 we get 8 by 9 into 9 plus 99 plus 999 plus 9999 plus so on. Now this is equal to 8 by 9 into 9 can be written as 10 minus 1 plus 99 can be written as 100 minus 1 plus 999 can be written as 1,000 minus 1 plus 9999 can be written as 10,000 minus 1 plus so on. This is equal to 8 by 9 into 10 plus 100 plus 1,000 plus so on up to n terms minus 1 plus 1 plus 1 plus so on up to n terms. Now this is equal to 8 by 9 into 10 plus we can write as 100 as 10 square 1000 as 10 q plus so on up to n terms minus 1 plus 1 plus 1 plus so on up to n terms. We know that sum of n terms of a GP that is Sn is equal to a into the power n minus 1 upon r minus 1 if r is greater than 1. So now this is equal to 8 by 9 into by using this formula sum of 10 plus 10 square plus 10 cube so on up to n terms is equal to 10 into 10 to the power n minus 1 upon 10 minus 1 minus n since 1 appears n times and this is equal to 8 by 9 into 10 into 10 to the power n minus 1 upon 9 minus n and this is equal to 80 upon 81 into n to the power n minus 1 minus 8 by 9 n hence the required sum is 80 by 81 into 10 to the power n minus 1 minus 8 by 9 n this is our required answer. So this completes the session. Bye and take care.