Find the sum of 7+77+777.......to infinity
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If 7+77+777.....to infinity, then the answer will also be upto infinite.
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(7/9){9+99+999+....+ to n terms}
(7/9){(10-1)+(100-1)+)(1000-1)+....+ to n term}
Separating the 10's and 1's .
(7/9){10+100+1000+.....+n terms-(1+1+1+...n terms)}
(7/9){10+100+1000+.... n terms-n}
(7/9){10(10n-1)/(9)-n} where a=10& r=10
(7/9){(10-1)+(100-1)+)(1000-1)+....+ to n term}
Separating the 10's and 1's .
(7/9){10+100+1000+.....+n terms-(1+1+1+...n terms)}
(7/9){10+100+1000+.... n terms-n}
(7/9){10(10n-1)/(9)-n} where a=10& r=10
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