Question

7+77+777+....................+n

Answer 1

Here is your answer...

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]

Answer 2

Sn = 7 / 9 [ ( 10 - 1 ) + ( 10^2 - 1 ) + ( 10^3 - 1 )...to n terms ]

Sn = 7 / 9 [ ( 10 + 10^2 + 10^3...+ 10^n ) - n ]

Sn = 7 / 9 [ 10( 10^n - 1 ) / ( 10 - 1 ) - n ]

Sn = 7 / 9 [ 10 / 9 { 10^n - 1 } - n ]

Sn = 7 / 81 [ 10^( n +1) - 9n - 10 ]