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Byju's Answer
Standard XI
Mathematics
Inequality
If a>b>1, the...
Question
If a > b > 1, then
a
n
−
b
n
>
n
(
a
−
b
)
for every + ive integer
n
≥
2
.
A
True
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B
False
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Solution
a
b
>
1
∴
1
+
a
b
+
a
2
b
2
+
…
…
(
a
b
)
n
−
1
>
n
as each is >1
Now sum a G.P. in L.H.S etc
a
n
−
b
n
b
n
−
1
(
a
−
b
)
>
n
or
a
n
−
b
n
>
n
(
a
−
b
)
b
n
−
1
>
n
(
a
−
b
)
as
b
>
1
⇒
b
n
−
1
>
1
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Similar questions
Q.
If a > b > 1, then
a
n
−
b
n
>
n
(
a
−
b
)
for every + ive integer
n
≥
2
.
Q.
If a , b are = ive , then from any integer n prove that
(
a
+
b
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n
<
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n
(
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)
Q.
Let
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I
such that
A
B
=
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is invertible for some positive integer
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A
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=
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−
B
n
+
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=
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+
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, then
Q.
If
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is an integer for every integer
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Q.
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