What is the sum of 1+11+111+1111+11111?
Well in the given case the sum can be easily found out, but imagine if there were some terms like the sum of1+11+111+1111+……………n termswhere n is a large number. Finding out the actual sum wouldn’t be feasible in such cases!So, I’ll be deriving a technique here to find the sum of such series with n terms, and will be finding out the required sum using it.Let,[math]S=1+11+111+1111+……….n terms[/math][math]9S=9+99+999+9999+..........n terms[/math][math]9S=(10-1)+(100-1)+(1000-1)........n terms[/math][math]9S=10+100+1000+10000+......n terms - n[/math]The above terms form a GP with,a=10 and common ratio(r)=10SO,[math]9S=\dfrac{10(10^n-1)}{10-1}-n[/math][math]S=\dfrac{1}{9}*(\dfrac{10(10^n-1)}{9}-n)[/math]Checking the formula for the question we’ve n=5.S=12345.So we can very well see that our method works.