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Mathematics
Mathematics
Problem
Let
a
=
3
1
/
124
+
1
a = 3^{1/124} + 1
a
=
3
1/124
+
1
and for all
n
≥
3
n \ge 3
n
≥
3
,
let
f
(
n
)
=
n
C
0
a
n
−
1
−
n
C
1
a
n
−
2
+
n
C
2
a
n
−
3
+
⋯
+
(
−
1
)
n
−
1
n
C
n
−
1
⋅
a
0
.
\text{let } f(n) = {}^n C_0 a^{n-1} - {}^n C_1 a^{n-2} + {}^n C_2 a^{n-3} + \dots + (-1)^{n-1} {}^n C_{n-1} \cdot a^0.
let
f
(
n
)
=
n
C
0
a
n
−
1
−
n
C
1
a
n
−
2
+
n
C
2
a
n
−
3
+
⋯
+
(
−
1
)
n
−
1
n
C
n
−
1
⋅
a
0
.
If the value of
f
(
2016
)
+
f
(
2017
)
=
3
K
f(2016) + f(2017) = 3^K
f
(
2016
)
+
f
(
2017
)
=
3
K
, the value of
K
K
K
is a. 6 b. 8 c. 9 d. 10
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