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3
Which is larger
Which is larger
Source: 2015 BAMO-8 #3, 2015 BAMO-12 #1
February 22, 2016
algebra
Fractions
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Problem Statement
Which number is larger,
A
A
A
or
B
B
B
, where
A
=
1
2015
(
1
+
1
2
+
1
3
+
⋯
+
1
2015
)
A = \dfrac{1}{2015} (1 + \dfrac12 + \dfrac13 + \cdots + \dfrac{1}{2015})
A
=
2015
1
(
1
+
2
1
+
3
1
+
⋯
+
2015
1
)
and
B
=
1
2016
(
1
+
1
2
+
1
3
+
⋯
+
1
2016
)
?
B = \dfrac{1}{2016} (1 + \dfrac12 + \dfrac13 + \cdots + \dfrac{1}{2016}) \text{ ?}
B
=
2016
1
(
1
+
2
1
+
3
1
+
⋯
+
2016
1
)
?
Prove your answer is correct.
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