1
If a > 1 then the arithmetic mean of a and 1/a
is
Answers
Answered by
2
Answer:
Step-by-step explanation:
a+1/a
=(a²+1)/a
so mean =(a²+1)/2a
Answered by
4
We know that arithmetic mean between a & b is
AM=
2
a+b
It is given that AM between a & b =
a
n−1
+b
n−1
a
n
+b
n
So,
a
n−1
+b
n−1
a
n
+b
n
=
2
a+b
2(a
n
+b
n
)=(a+b)(a
n−1
+b
n−1
)
2a
n
+2b
n
=a(a
n−1
+b
n−1
)+b(a
n−1
+b
n−1
)
2a
n
+2b
n
=aa
n−1
+ab
n−1
+ba
n−1
+bb
n−1
2a
n
+2b
n
=a
n
+ab
n
−1+ba
n−1
+b
n
a
n
+b
n
−ab
n−1
−a
n−1
b=0
a.a
n−1
−a
n−1
b+b.b
n−1
−ab
n−1
=0
a
n−1
(a−b)−b
n−1
(a−b)=0
(a
n−1
−b
n−1
)(a−b)=0
a−b=0
a=b [not possible as a
=b]
∴a
n−1
−b
n−1
=0
a
n−1
=b
n−1
b
n−1
a
n−1
=1
(
b
a
)
n−1
=(
b
a
)
0
[As(
b
a
)
0
=1]
Comparing powers
n−1=0
n=1
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