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Mathematics
Problem
Explain briefly why, for a positive decreasing function
f
f
f
, the value of
∫
1
∞
f
(
x
)
d
x
\displaystyle\int_{1}^{\infty} f(x)\,dx
∫
1
∞
f
(
x
)
d
x
must be less than or equal to
∑
n
=
1
∞
f
(
n
)
\displaystyle\sum_{n=1}^{\infty} f(n)
n
=
1
∑
∞
f
(
n
)
.
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