7 + 77 + 777 + .............+7777..77(n digits) = 7/81(10ⁿ⁺¹ -9n -10)

[Karthik]

show that

7 + 77 + 777 + …+7777…77(n digits) = 7/81(10ⁿ⁺¹ -9n -10)