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Abel's Inequality


Let {f_n} and {a_n} be sequences with f_n>=f_(n+1)>0 for n=1, 2, ..., then

 |sum_(n=1)^ma_nf_n|<=Af_1,

where

 A=max{|a_1|,|a_1+a_2|,...,|a_1+a_2+...+a_m|}.

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Cite this as:

Weisstein, Eric W. "Abel's Inequality." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/AbelsInequality.html

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