If the set of non zero numbers 1-a1-1-a2-1-an are in A-P- then the set of numbers an-a1-a2-an-1-a2-a1-a3-an-a1-a2-a3-an

The correct option is C H.PSince, 1 a_ 1 , 1 a_ 2 ,⋯ , 1 a_ n nbsp; are in A.P. ∴ a_ n +a_ n 1 +...a_ 2 a_ 1 +1, a_ n +a_ n 1 +...+a_ 1 ...

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Change of Variables

If the set of...

Question

If the set of non zero numbers $\frac{1}{a_{1}}, \frac{1}{a_{2}}, \dots \frac{1}{a_{n}}$ are in A.P. then the set of numbers $\frac{a_{n}}{a_{1} + a_{2} + \dots + a_{n - 1}}, . . . . ., \frac{a_{2}}{a_{1} + a_{3} + \dots + a_{n}} + \frac{a_{1}}{a_{2} + a_{3} + \dots + a_{n}}$

G.P.

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H.P

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A.P.

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None of these

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a_{1}, a_{2}, a_{3}, . . ., a_{n}

\frac{1}{a_{1} a_{2}} + \frac{1}{a_{2} a_{3}} + \frac{1}{a_{3} a_{4}} + . . . \frac{1}{a_{n - 1} a_{n}} = \frac{n - 1}{a_{1} a_{n}}

a_{1}, a_{2}, a_{3}, . . . . a_{n}

\frac{1}{\sqrt{a_{1}} + \sqrt{a_{2}}} + \frac{1}{\sqrt{a_{2}} + \sqrt{a_{3}}} + . . . + \frac{1}{\sqrt{a_{n - 1}} + \sqrt{a_{n}}}

a_{1}, a_{2}, a_{3}, . . . . . a_{n}

\frac{a_{1}}{a_{2} + a_{3} + . . . a_{n}}, \frac{a_{2}}{a_{1} + a_{3} + . . . . + a_{n}}, \frac{a_{n}}{a_{1} + a_{2} + . . . + a_{n - 1}}

a_{1}, a_{2}, a_{3}, . . . . a_{n}

\frac{a_{1}}{a_{2} + a_{3} + . . . . + a_{n}}, \frac{a_{2}}{a_{1} + a_{3} + . . . . + a_{n}}, . . . ., \frac{a_{n}}{a_{1} + a_{2} + . . . . + a_{n - 1}}

a_{1}, a_{2}, a_{3}, . . . . . . . a_{n}

a_{1} > 0

\forall

\frac{1}{\sqrt{a_{1}} + \sqrt{a_{2}}} + \frac{1}{\sqrt{a_{2}} + \sqrt{a_{3}}} + . . . . . + \frac{1}{\sqrt{a_{n - 1}} + \sqrt{a_{n}}} = \frac{k}{\sqrt{a_{1}} + \sqrt{a_{n}}}

k

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