MathDB
Problems
Contests
National and Regional Contests
Hungary Contests
Eotvos Mathematical Competition (Hungary)
1941 Eotvos Mathematical Competition
1
1
Part of
1941 Eotvos Mathematical Competition
Problems
(1)
prod (1 + x) ... (1 + x^2{k-1} )
Source: Eotvos 1941 p1
9/10/2024
Prove that
(
1
+
x
)
(
1
+
x
2
)
(
1
+
x
4
)
(
1
+
x
8
)
.
.
.
(
1
+
x
2
k
−
1
)
=
1
+
x
+
x
2
+
x
3
+
.
.
.
+
x
2
k
−
1
(1 + x)(1 + x^2)(1 + x^4)(1 + x^8) ... (1 + x^{2^{k-1}} ) = 1 + x + x^2 + x^3 +... + x^{2^{k-1}}
(
1
+
x
)
(
1
+
x
2
)
(
1
+
x
4
)
(
1
+
x
8
)
...
(
1
+
x
2
k
−
1
)
=
1
+
x
+
x
2
+
x
3
+
...
+
x
2
k
−
1
algebra
Product