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Definite Integral as Limit of Sum

If a,b,c ar...

Question

If $a, b, c$ are in HP then(consider $n > 0$ )

a^{n} + c^{n} > b^{n}

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a^{n} + c^{n} > 2 b^{n}

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a^{n} + b^{n} > 2 c^{n}

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b^{n} + c^{n} > 2 a^{n}

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Solution

The correct option is B $a^{n} + c^{n} > 2 b^{n}$

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Similar questions

a, b, c

(a^{n} + b^{n}), (b^{n} + c^{n}), (c^{n} + d^{n})

If a, b, c, d are in G.P., prove that $(a^{n} + b^{n}), (b^{n} + c^{n}), (c^{n} + d^{n})$ are in G.P.

(a^{n} + b^{n}), (b^{n} + c^{n}), (c^{n} + d^{n})

a, b, c, d

(a^{n} + b^{n}), (b^{n} + c^{n}), (c^{n} + d^{n})

{a_{n}}, {b_{n}}, {c_{n}}

(i) a_{n} + b_{n} {+ c}_{n} = 2 n + 1

(i i) a_{n} b_{n} + b_{n} c_{n} + {+ c}_{n} a_{n} = 2 n - 1

(i i i) a_{n} b_{n} c_{n} = - 1

(i v) a_{n} < b_{n} < c_{n}

lim n \to \infty n a_{n}

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