By using Binomial theorem P.T 2^2n-3n-1 is
divisible by 9
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Answer:
ANSWER
2 3n−7n−1=(2 3
) n
−7n−1
=8
n
−7n−1
=(1+7)
n
−7n−1
Binomial theorem,
(x+a)
n
=
n
C
0
x
n
a
0
+
n
C
1
x
n−1
a
1
+
n
C
2
x
n−2
a
2
+...+
n
C
r
x
n−r
a
r
+.......+a
n
∴2
3n
−7n−1
=
n
C
0
7
0
+
n
C
1
7
1
+
n
C
2
7
2
+...+
n
C
n
7
n
−7n−1
=1+
(n−1)!
n!
×7+7
2
(
n
C
2
+
n
C
37+...+
nCn7
n−2
)−7n−1
=n×7−7n+7 2 ( nC 2+ nC 3
7+...+ nC n
7 n−2)=49(
nC2
+
nC 3
7+...+ nC n7 n−2 )
=49K (multiple of 49)
Hence, divisible by 49.
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