MathDB
Problems
Contests
National and Regional Contests
USA Contests
MAA AMC
AMC 10
2022 AMC 10
1
Finitely Nested Fractions
Finitely Nested Fractions
Source: 2022 AMC 10A #1 / 2022 AMC 12A #1
November 11, 2022
2022 AMC
2022 AMC 10a
2022 AMC 12A
AMC 10
AMC 12
AMC
Fractions
Problem Statement
What is the value of
3
+
1
3
+
1
3
+
1
3
?
3 + \frac{1}{3+\frac{1}{3+\frac{1}{3}}}?
3
+
3
+
3
+
3
1
1
1
?
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
a
n
>
31
10
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
a
n
>
49
15
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
a
n
>
33
10
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
a
n
>
109
33
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
a
n
>
15
4
<span class='latex-bold'>(A) </span> \frac{31}{10} \qquad <span class='latex-bold'>(B) </span> \frac{49}{15} \qquad <span class='latex-bold'>(C) </span> \frac{33}{10} \qquad <span class='latex-bold'>(D) </span> \frac{109}{33} \qquad <span class='latex-bold'>(E) </span> \frac{15}{4}
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
an
>
10
31
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
an
>
15
49
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
an
>
10
33
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
an
>
33
109
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
an
>
4
15
Back to Problems
View on AoPS