4. Suppose that f : R -+ (0,00) is differentiable, f(x) -+ 0 as x -+ 00,...
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4. Suppose that f : R -+ (0,00) is differentiable, f(x) -+ 0 as x -+ 00, and
. xf'(x)
a:= lIm -f() X--+OO x exists. If a < -1, prove that 2:;:'=1 f(k) converges.
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