of the
Week
|
Problem
of the Week |
Show that none of the polynomials p0(x), p2(x), p4(x),... defined by the formula
p2n(x) = 1 + x + x2/2! + x3/3! + x4/4! +...+ x2n-1/(2n-1)! + x2n/(2n)!
has a real root; that is, show that their graphs never
cross the
x-axis.
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