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Byju's Answer
Standard XII
Physics
Optical Fiber
If H1,H2,.....
Question
If
H
1
,
H
2
,
.
.
.
,
H
n
are the
n
harmonic means between
a
and
b
, then
H
1
+
a
H
1
−
a
+
H
n
+
b
H
n
−
b
=
A
n
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B
n
+
1
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C
2
n
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D
2
n
−
2
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Solution
The correct option is
B
2
n
Given
H
1
,
H
2
,
.
.
.
,
H
n
are the
n
harmonic means between
a
and
b
,
∴
1
H
n
=
1
b
−
d
,
1
H
1
=
1
a
+
d
H
1
+
a
H
1
−
a
+
H
n
+
b
H
n
−
b
=
1
a
+
1
H
1
1
a
−
1
H
1
+
1
b
+
1
H
n
1
b
−
1
H
n
=
1
a
+
1
a
+
d
1
a
−
d
−
1
a
+
1
b
+
1
b
−
d
1
b
+
d
−
1
b
=
2
a
+
d
−
d
+
2
b
−
d
d
=
2
b
−
2
a
d
−
2
=
2
(
n
+
1
)
−
2
[
∵
1
b
=
1
a
+
(
n
+
2
−
1
)
d
]
=
2
n
Suggest Corrections
1
Similar questions
Q.
If
H
1
,
H
2
,
.
.
.
.
,
H
n
are n harmonic means between a and b(
≠
a), then the value of
H
1
+
a
H
1
−
a
+
H
n
+
b
H
n
−
b
=
Q.
Assertion :
H
1
,
H
2
,
H
3
,
.
.
.
.
H
n
be
n
H
.
M
between
a
and
b
then value of
H
1
+
a
H
1
−
a
+
H
n
+
b
H
n
−
b
=
2
n
Reason:
H
1
=
(
n
+
1
)
a
b
n
b
+
a
,
H
n
=
(
n
+
1
)
a
b
n
a
+
b
obtained by interchanging the numbers
a
&
b
.
Q.
If
n
arithmetic means
a
1
,
a
2
,
.
.
.
,
a
n
are inserted between
50
and
200
and
n
harmonic means
h
1
,
h
2
,
.
.
.
,
h
n
are inserted between the same two numbers, then
(
a
2
h
n
−
1
÷
2000
)
is equal to
Q.
If a,
H
1
,
H
2
,
.
.
.
.
.
.
.
,
H
n
,
b
are in H.P., then
1
a
,
1
H
1
,
1
H
2
,
.
.
.
.
.
.
.
.
.
.
,
1
H
n
,
1
b
are in A.P., whose common difference is
a
−
b
(
n
+
1
)
a
b
.
Q.
Let
n
≥
1
be a positive integer. Suppose, between two distinct positive real numbers
k
and
l
,
n
arithmetic means
a
1
,
a
2
,
.
.
.
,
a
n
and
n
harmonic means
h
1
,
h
2
,
.
.
.
.
,
h
n
are inserted. For
i
=
1
,
2
,
.
.
.
.
,
n
and
j
=
1
,
2
,
.
.
.
.
,
n
, let
p
(
i
,
j
)
=
a
i
h
j
then
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