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Mathematics
Problem
State the three conditions on a function
f
(
x
)
f(x)
f
(
x
)
defined for
x
≥
1
x\ge 1
x
≥
1
that must be verified before one may compare
∑
n
=
1
∞
f
(
n
)
\displaystyle\sum_{n=1}^{\infty} f(n)
n
=
1
∑
∞
f
(
n
)
with the improper integral
∫
1
∞
f
(
x
)
d
x
\int_{1}^{\infty} f(x)\,dx
∫
1
∞
f
(
x
)
d
x
for the purpose of determining convergence.
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