|f(a * 2^n) / 2^n - f(a * 2^m) / 2^m|

=

(1 / 2^n) * |f(a * 2^n) - 2^(n - m) * f(a * 2^m)|

=

(1 / 2^n) * |f(a * 2^m * 2^(n - m)) - 2^(n - m) * f(a * 2^m)|

=

(1 / 2^n) * |f(a * 2^m) + … + f(a * 2^m) - f(a * 2^m) - … - f(a * 2^m)|

<

(1 / 2^n) * K (for some positive real number K)



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