MathDB

Sum of 9's

Source: USAMO 1992

October 27, 2005

functioninductiongeometric seriesnumber theory unsolvednumber theory

Problem Statement

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.