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Problems
Contests
National and Regional Contests
USA Contests
MAA AMC
AMC 12/AHSME
1968 AMC 12/AHSME
5
5
Part of
1968 AMC 12/AHSME
Problems
(1)
Adding Functions
Source: 1968 AHSME Problem #5
8/31/2011
If
f
(
n
)
=
1
3
n
(
n
1
)
(
n
+
2
)
f(n)=\tfrac{1}{3}n(n1)(n+2)
f
(
n
)
=
3
1
n
(
n
1
)
(
n
+
2
)
, then
f
(
r
)
−
f
(
r
−
1
)
f(r)-f(r-1)
f
(
r
)
−
f
(
r
−
1
)
equals:
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
a
n
>
r
(
r
+
1
)
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
a
n
>
(
r
+
1
)
(
r
+
2
)
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
a
n
>
1
3
r
(
r
+
1
)
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
a
n
>
1
3
(
r
+
1
)
(
r
+
2
)
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
a
n
>
1
3
r
(
r
+
1
)
(
r
+
2
)
<span class='latex-bold'>(A)</span>\ r(r+1) \qquad <span class='latex-bold'>(B)</span>\ (r+1)(r+2) \qquad <span class='latex-bold'>(C)</span>\ \tfrac{1}{3}r(r+1) \qquad\\ <span class='latex-bold'>(D)</span>\ \tfrac{1}{3}(r+1)(r+2) \qquad <span class='latex-bold'>(E)</span>\ \tfrac{1}{3}r(r+1)(r+2)
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
an
>
r
(
r
+
1
)
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
an
>
(
r
+
1
)
(
r
+
2
)
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
an
>
3
1
r
(
r
+
1
)
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
an
>
3
1
(
r
+
1
)
(
r
+
2
)
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
an
>
3
1
r
(
r
+
1
)
(
r
+
2
)
function
AMC