Suppose that f(x) is positive, continuous, decreasing
function on the interval
[N, ). Let
a n = f(n). Then
converges if and only if
converges
Context
Note that this test is much different from all the others. We have not
yet formally introduced the concept of an Integral - or even of a
continuous function - so that we can not prove this test here. However,
for completeness it is included as a test that is sometimes useful to
apply.
Interactive Real Analysis, ver. 1.9.5 (c) 1994-2007, Bert G. Wachsmuth Page last modified: Mar 28, 2007
). Let a n = f(n). Then
converges if and only if
converges
Context