4 + 44 + 444 + ...n terms
= 4 [ 1 + 11 + 111 + ... n terms ]
= (4/9) [ 9 + 99 + 999 + ... n terms ]
= (4/9) [ (10 - 1) + (102 - 1) + (103 - 1) + ... + (10n - 1) ]
= (4/9) [ ( 10 + 102 + 10n + ... + 10n ) - ( 1 + 1 + 1 + ... n times ) ]
= (4/9) { 10 [ ( 10n - 1 ) / ( 10 - 1 ) ] - n(1) }
= (4/9) [ (10/9) ( 10n - 1 ) - n ]