Question

Let \(a>b>0\) and \(I(n)=a^{\gamma}-b^{\gamma}, J(n)=(a-b)^{\gamma}\) for all \(n \geq 2\). Then
(A) \(I(n)<J(n)\)
(B) \(I(n)>J(n)\)
(C) \(I(n)=J(n)\)
(D) \(I(n)+J(n)=0\)

Answer 1

Ans: (A)
Hint \(: \frac{I(n)}{J(n)}=\frac{a^{y}-b^{y}}{(a-b)^{Y / n}}=\frac{x^{Y / n}-1}{(x-1)^{Y_{n}}}=\lim _{x \rightarrow 1^{+}} \frac{I(n)}{J(n)}=\lim _{x \rightarrow 1}\left(1-\frac{1}{x}\right)^{\left(1-\frac{1}{n}\right)} \quad \because x>0 \& n \geq 2\)

Answer 2

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Answer 3

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