More and more threes

Algebra Level 4

3,33,333,,333333n number of 3’s 3,33,333,\ldots, \underbrace{33333\ldots3}_{n \text{ number of 3's}}

Given that the sum of the nn number of terms above is equal to

1a(bn+1cnd) \frac 1a (b^{n+1} - cn - d )

for positive integers a,b,ca,b,c and dd. Find the value of a+b+c+d+1a+b+c+d+1.

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