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Omni-MATH / Find, as a function of n, the sum of the digits of 9×99×9999×⋯×(10^(2^(n))−1), where each factor has twice as many digits as the previous one.

Problem

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problem

Find, as a function of n,\, n, \, the sum of the digits of 9×99×9999×⋯×(102n−1),9 \times 99 \times 9999 \times \cdots \times \left( 10^{2^n} - 1 \right), where each factor has twice as many digits as the previous one.
Plain-text mathematical notation (without MathML)
Find, as a function of  n,  the sum of the digits of 9×99×9999×⋯×(10^(2^(n))−1), where each factor has twice as many digits as the previous one.
Original LaTeX notation
Find, as a function of $\, n, \,$ the sum of the digits of \[9 \times 99 \times 9999 \times \cdots \times \left( 10^{2^n} - 1 \right),\] where each factor has twice as many digits as the previous one.

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Source and history

task_id
b24a950f-9c83-5026-ba6f-6fa7595b8f72
task_key
test--b24a950f-9c83-5026-ba6f-6fa7595b8f72
task_revision_id
1
config / split
/ test

Official source

initial import