1. Let x=0.1.234567891011121314151617181912021...
(a) Find the 2011th digit after the decimal point of x.
(b) Show that x is irrational
2. There are 92 airports in Illinois. Suppose a flight takes off at each airport and lands in the nearest neighbouring airport. Assuming that mutual distances between the airports are all distinct, prove that there is no airport at which more than five planes land.
3. Find a simple formula (with proof) of the sum S_n = \sum_1^n k/(k+1)!
(a) Find the 2011th digit after the decimal point of x.
(b) Show that x is irrational
2. There are 92 airports in Illinois. Suppose a flight takes off at each airport and lands in the nearest neighbouring airport. Assuming that mutual distances between the airports are all distinct, prove that there is no airport at which more than five planes land.
3. Find a simple formula (with proof) of the sum S_n = \sum_1^n k/(k+1)!
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