MathDB
Problems
Contests
National and Regional Contests
India Contests
India LIMIT
2019 LIMIT
2019 LIMIT Category C
Problem 7
Problem 7
Part of
2019 LIMIT Category C
Problems
(2)
infinite fraction sum
Source: LIMIT 2019 CCS1 P7
4/28/2021
The value of
(
1
+
2
6
+
2
⋅
5
6
⋅
12
+
2
⋅
5
⋅
8
6
⋅
12
⋅
18
+
…
)
3
\left(1+\frac26+\frac{2\cdot5}{6\cdot12}+\frac{2\cdot5\cdot8}{6\cdot12\cdot18}+\ldots\right)^3
(
1
+
6
2
+
6
⋅
12
2
⋅
5
+
6
⋅
12
⋅
18
2
⋅
5
⋅
8
+
…
)
3
Summation
algebra
4x4 orthogonal matrices over Z
Source: LIMIT 2019 CCS2 P7
4/28/2021
Let
O
(
4
,
Z
)
O(4,\mathbb Z)
O
(
4
,
Z
)
be the set of all
4
×
4
4\times4
4
×
4
orthogonal matrices over
Z
\mathbb Z
Z
, i.e.,
A
t
A
=
I
=
A
A
t
A^tA=I=AA^t
A
t
A
=
I
=
A
A
t
. Then
∣
O
(
4
,
Z
)
∣
|O(4,\mathbb Z)|
∣
O
(
4
,
Z
)
∣
is
Matrices
linear algebra