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MAA AMC
AMC 12/AHSME
1966 AMC 12/AHSME
25
Funny Function
Funny Function
Source:
March 25, 2006
function
Problem Statement
If
F
(
n
+
1
)
=
2
F
(
n
)
+
1
2
F(n+1)=\frac{2F(n)+1}{2}
F
(
n
+
1
)
=
2
2
F
(
n
)
+
1
for
n
=
1
,
2
,
…
n=1,2,\ldots
n
=
1
,
2
,
…
, and
F
(
1
)
=
2
F(1)=2
F
(
1
)
=
2
, then
F
(
101
)
F(101)
F
(
101
)
equals:
(A)
49
(B)
50
(C)
51
(D)
52
(E)
53
\text{(A)} \ 49 \qquad \text{(B)} \ 50 \qquad \text{(C)} \ 51 \qquad \text{(D)} \ 52 \qquad \text{(E)} \ 53
(A)
49
(B)
50
(C)
51
(D)
52
(E)
53
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