 of sum of GP last year 0.3 bar how much was it how much it how much was it you found out right rational expression for 0.3 bar in P by Q form what was 3 by 1 by 3 right they will use of sum of infinite GP can be used to find out the same now let us say s is equal to 0.33333 this is the thing can I write this as s 0.3 plus 0.03 plus 0.003 plus 0.0003 plus 1 and so forth right I can write that I can write that as 3 upon 10 plus 3 upon 100 plus 3 upon 1000 plus 3 upon 10,000 plus 1 and so forth till infinity is it it so s cannot take 3 by 10 common and I will get 1 plus 1 by 10 plus 1 by 100 plus 1 by 1000 plus so on and so forth till infinity now is this finite or infinite series with what is the ratio this is an infinite series infinite series right what is the ratio ratio is what is the common ratio in this case what is the common ratio ratio is 1 upon 10 so what will be the sum sum is a upon 1 minus r right a is 1 1 minus 1 by 10 which is 3 by 10 into 10 by 9 once again understood last class in grade 9 whatever we learnt finding out the you know p by q form of a recurrent non-terminating decimal form so you can use that now find this sum 5 55 55 55 55 55 55 2 in terms get me an expression for this so let's say 5 plus 55 let's say this is s plus 555 dot dot what will you do till n terms let's say you are doing for n terms not infinite there is no question of infinite series here because infinite series will make it infinity anyways positive ratio r would be higher right more than right so take 5 common so what will you get 1 plus 11 plus 111 plus 1111 plus dot dot dot n terms right but we have still not yeah why not can I take 5 common from all what is the problem 5 into 1 5 into 11 5 into 1 1 1 what is the problem you give it okay yep so now but still this is not in GP not in GP but we can convert it into one how 5 okay so you can write this as how how will you write this yeah you can do this you can multiply divide by 9 so this becomes 9 99 9 9 9 9 9 9 9 10 terms is it is that okay can I do that multiply and divide the entire thing by 9 correct no you are in TSC they can ask you what is the value till 20 terms like that is it okay or give it by with the put okay say next year 5 by 9 can I write 9 as 10 minus 1 right and 99 as 100 minus 1 and triple 9 as 1000 minus 1 right and 1 0 0 0 0 minus 1 like correct now do you see some GP 5 by 9 then 10 100,000 right till n terms right and then minus 1 so all minus common 1 plus 1 plus 1 plus 1 how many n terms right so as it is 5 by 9 or the sum of this GP is first term into common ratio is 10 to the power n minus 1 by 10 minus 1 which is 9 minus n am I right this is the expression for some till n terms below so much guy did you understand so if you want you can simplify it further so what you can do is take LCM so 5 by 81 so this 9 comes out but in return what does it do it becomes 10 to the power n plus 1 minus 10 minus 9 n this is a term for some of that series and it's done below