Question

Find the sum of first n terms of the series.   7+77+777+.......

Answer 1

7, 77, 777, 7777 ….to n terms.         
Sn=7+77+777+7777+……+to n terms      
introducing 9       
  = (7/9) [9+99+999+……+ to n terms]              
= (7/9) [(10-1) + (100-1) + (1000-1) +……...+ to n term]               
= (7/9) [10+100+1000+……... n terms – (1+1+1+1+…… n terms)             
  = (7/9) [10+100+1000+………n terms –n]     
 Here      a=10, r=10             
 = (7/9) [10(10n-1)/ (9) - n]

Answer 2

Sn=7+77+777+7777+……+to n terms            
  = (7/9) [9+99+999+……+ to n terms]               
= (7/9) [(10-1) + (100-1) + (1000-1) +……...+ to n term]               
= (7/9) [10+100+1000+……... n terms – (1+1+1+1+…… n terms)             
  = (7/9) [10+100+1000+………n terms –n]     
  a=10, r=10             
 = (7/9) [10(10 n-1)/ (9) - n]