2026 AIME II Problem 9

Let S denote the value of the infinite sum\frac 19 + \frac 1{99} + \frac 1{999} + \frac 1{9999} + \cdotsFind the remainder when the greatest integer less than or equal to 10^{100} S is divided by 1000.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.