MathDB
Problems
Contests
National and Regional Contests
India Contests
India LIMIT
2019 LIMIT
2019 LIMIT Category B
Problem 10
Problem 10
Part of
2019 LIMIT Category B
Problems
(2)
counting six-digit numbers with 239 and 6|n
Source: LIMIT 2019 CBS1 P10
4/28/2021
Using only the digits
2
,
3
2,3
2
,
3
and
9
9
9
, how many six-digit numbers can be formed which are divisible by
6
6
6
?
combinatorics
sum of 1/(√n+√(n+2))
Source: LIMIT 2019 CBS2 P10
4/28/2021
1
1
+
3
+
1
3
+
5
+
1
5
+
7
+
…
+
1
2017
+
2019
=
?
\frac1{1+\sqrt3}+\frac1{\sqrt3+\sqrt5}+\frac1{\sqrt5+\sqrt7}+\ldots+\frac1{\sqrt{2017}+\sqrt{2019}}=?
1
+
3
1
+
3
+
5
1
+
5
+
7
1
+
…
+
2017
+
2019
1
=
?
<
s
p
a
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c
l
a
s
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=
′
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a
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−
b
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>
(
A
)
<
/
s
p
a
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>
2019
−
1
2
<span class='latex-bold'>(A)</span>~\frac{\sqrt{2019}-1}2
<
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a
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=
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−
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(
A
)
<
/
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p
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>
2
2019
−
1
<
s
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c
l
a
s
s
=
′
l
a
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x
−
b
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′
>
(
B
)
<
/
s
p
a
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>
2019
+
1
2
<span class='latex-bold'>(B)</span>~\frac{\sqrt{2019}+1}2
<
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p
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a
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=
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(
B
)
<
/
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p
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>
2
2019
+
1
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
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′
>
(
C
)
<
/
s
p
a
n
>
2019
−
1
4
<span class='latex-bold'>(C)</span>~\frac{\sqrt{2019}-1}4
<
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p
an
c
l
a
ss
=
′
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a
t
e
x
−
b
o
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′
>
(
C
)
<
/
s
p
an
>
4
2019
−
1
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
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x
−
b
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>
(
D
)
<
/
s
p
a
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>
None of the above
<span class='latex-bold'>(D)</span>~\text{None of the above}
<
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b
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(
D
)
<
/
s
p
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>
None of the above
Summation
algebra