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2023 UMD Math Competition Part I
#6
#6
Part of
2023 UMD Math Competition Part I
Problems
(1)
Let and what
Source: UMD 2023 I #6
10/27/2023
Let
A
=
log
(
1
)
+
log
2
+
log
(
3
)
+
⋯
+
log
(
2023
)
A = \log (1) + \log 2 + \log(3) + \cdots + \log(2023)
A
=
lo
g
(
1
)
+
lo
g
2
+
lo
g
(
3
)
+
⋯
+
lo
g
(
2023
)
and
B
=
log
(
1
/
1
)
+
log
(
1
/
2
)
+
log
(
1
/
3
)
+
⋯
+
log
(
1
/
2023
)
.
B = \log(1/1) + \log(1/2) + \log(1/3) + \cdots + \log(1/2023).
B
=
lo
g
(
1/1
)
+
lo
g
(
1/2
)
+
lo
g
(
1/3
)
+
⋯
+
lo
g
(
1/2023
)
.
What is the value of
A
+
B
?
A + B\ ?
A
+
B
?
(
(
(
logs are logs base
10
)
10)
10
)
a
.
0
b
.
1
c
.
−
log
(
2023
!
)
d
.
log
(
2023
!
)
e
.
−
2023
\mathrm a. ~ 0\qquad \mathrm b.~1\qquad \mathrm c. ~{-\log(2023!)} \qquad \mathrm d. ~\log(2023!) \qquad \mathrm e. ~{-2023}
a
.
0
b
.
1
c
.
−
lo
g
(
2023
!)
d
.
lo
g
(
2023
!)
e
.
−
2023
UMD
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