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Question

If a > b > 1, then anbn>n(ab) for every + ive integer n2.

A
True
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B
False
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Solution

ab>1
1+ab+a2b2+(ab)n1>n as each is >1
Now sum a G.P. in L.H.S etc
anbnbn1(ab)>n
or anbn>n(ab)bn1
>n(ab)
as b>1bn1>1

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