Question

find the sum of n terms of the series 7+77+777+................upto n terms

Answer 1

(7/9)[10(10n-1)/(9)-n]

Answer 2

7 + 77 + 777 +.........
7[1 + 11 + 111 + ..........]

7/9[9 + 99 + 999 +.......]

7/9[(10-1) + (100-1) + (1000-1).......]

7/9[(10 + 100 + 1000.....) - (1+1+1........)]

7/9[ {10(10^n - 1)/(10-1)} - n]

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

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

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

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