MathDB
Problems
Contests
National and Regional Contests
Moldova Contests
JBMO TST - Moldova
2007 Junior Balkan Team Selection Tests - Moldova
8
(1+1/2)(1+1/3)(1+1/4)...(1+1/2006)(1+1/2007)
(1+1/2)(1+1/3)(1+1/4)...(1+1/2006)(1+1/2007)
Source: 2007 Moldova JBMO TST p8
February 20, 2021
Product
algebra
combinatorics
Problem Statement
a) Calculate the product
(
1
+
1
2
)
(
1
+
1
3
)
(
1
+
1
4
)
.
.
.
(
1
+
1
2006
)
(
1
+
1
2007
)
\left(1+\frac{1}{2}\right) \left(1+\frac{1}{3}\right) \left(1+\frac{1}{4}\right)... \left(1+\frac{1}{2006}\right) \left(1+\frac{1}{2007}\right)
(
1
+
2
1
)
(
1
+
3
1
)
(
1
+
4
1
)
...
(
1
+
2006
1
)
(
1
+
2007
1
)
b) Let the set
A
=
{
1
2
,
1
3
,
1
4
,
.
.
.
,
1
2006
,
1
2007
}
A =\left\{\frac{1}{2}, \frac{1}{3},\frac{1}{4}, ...,\frac{1}{2006}, \frac{1}{2007}\right\}
A
=
{
2
1
,
3
1
,
4
1
,
...
,
2006
1
,
2007
1
}
Determine the sum of all products of
2
2
2
, of
4
4
4
, of
6
6
6
,... , of
2004
2004
2004
¸and of
2006
2006
2006
different elements of the set
A
A
A
.
Back to Problems
View on AoPS