So many nines causes irritation.

Algebra Level 4

9 × 99 × 9999 × . . . × ( 10 2 2018 1 ) \large\ 9\times 99\times 9999\times ...\times \left( { 10 }^{ { 2 }^{ 2018 } } - 1 \right)

Find the sum of the digits of the expression above, where each factor has twice as many digits as the previous one.

9 × 2 2018 2 2017 9\times2^{2018} - 2^{2017} 9 × 2 2018 9\times2^{2018} 3 × 2 2018 3\times2^{2018} 2 × 9 2018 2\times9^{2018} 9 × 2 2017 9\times2^{2017}

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