Answers

  • Brainly User
2015-02-20T22:49:28+05:30
7+77+777....n terms =7(1+11+111+.....n terms) Divide n multiply by 9 7×9/9(1+11+111+. ..n terms) 7/9(9+99+999...n terms) 7/9[(10-1)+(100-1)+(1000-1)...n terms] 7/9[10+100+1000...n terms-(1+1+1+...n terms]_(1●) First consider 10+100+.... Sn=10[10^n-1/10-1] =》10/9(10^n-1) sn=>7/9{10/9(10^n-1)-n} =>70/81(10^n-1)-7/9n) Now consider 1+1.. Sn=n Sn=
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2015-02-21T05:25:11+05:30
7+77+777....n terms
 
=7(1+11+111+.....n terms)
 
 multiply with 9/9  .....

7×9/9(1+11+111+. ..n terms)

7/9(9+99+999...n terms)
 
7/9[(10-1)+(100-1)+(1000-1)...n terms]
 
7/9[  (10+100+1000...n terms)  -   (1+1+1+...n terms)  ]

Sn  =   7/9{10/9(10^n-1)-n}
 
 
 7+77+777.....= 70/81(10^n-1)-7/9n) 


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