## Tuesday, January 9, 1990

### 1990 - 19 & 20

This new set is from the 1990 test.

Difficulty: Medium. I didn't bother with this one - too lazy. Anyone? Post them in the comments for the answer sheet !

Difficulty: Medium because of time pressure. Easy to understand, though. A good one for all levels.

Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest 2013

Latex test:

What is $\dfrac{9}{10}+\dfrac{9}{100}+\dfrac{9}{1000}+\dfrac{9}{10000}+ ...$?
Put another way, what is the value of $0.\overline{9}$ or $0.999999 ...$?