Find the sum of sequence 7 , 77 , 777 , 7777,.....to 'n' terms

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(10 ^n−1)/9−n]

= 70/81 (10 ^n −1)−n