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Mathematics
Mathematics
Problem
List the three conditions a function
f
(
x
)
f(x)
f
(
x
)
must satisfy on
[
1
,
∞
)
[1,\infty)
[
1
,
∞
)
so that one may compare the infinite series
∑
n
=
1
∞
f
(
n
)
\sum_{n=1}^{\infty} f(n)
∑
n
=
1
∞
f
(
n
)
with the improper integral
∫
1
∞
f
(
x
)
d
x
\displaystyle \int_{1}^{\infty} f(x)\,dx
∫
1
∞
f
(
x
)
d
x
when deciding convergence.
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