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For a series , if there exists a function , such that
Then we have the series converges if and only if the improper integral converges.
If the series converges, compare the three values : , ,
, if there exists a function 
, such that 
is positive on 
is continuous on 
is decreasing on 
,
converges if and only if the improper integral 
converges. 
, 
, 
