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Indian Institute of Foreign Trade 2008 Solved Paper
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© examsnet.com
Question : 34
Total: 150
If
H
1
,
H
2
,
H
3
,.......,
H
n
are 'n' Harmonic means between ‘a’ and ‘b’ (≠ a), then value of
(
H
1
+
a
)
(
H
1
−
a
)
+
(
H
n
+
b
)
(
H
n
−
b
)
is equal to
n+1
2n
2n+3
n-1
Validate
Solution:
Let us assume that n = 3 and a, b = 2, 6.
Therefore, the harmonic sequence will be: 2,
H
1
,
H
2
,
H
3
,6
Hence,
H
2
=
(
2
*
2
*
6
)
(
2
+
6
)
=3
H
1
=
(
2
*
2
*
3
)
(
2
+
3
)
=2.4
H
3
=
(
2
*
3
*
6
)
(
3
+
6
)
=4
Therefore,
(
H
1
+
a
)
(
H
1
−
a
)
+
(
H
n
+
b
)
(
H
n
−
b
)
(
2.4
+
2
)
(
2.4
−
2
)
+
(
4
+
6
)
(
4
−
6
)
⇒11-5 = 6
Option B: 2n = 2*3 = 6.
© examsnet.com
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