If a-a1-a2-a3-a2n-b are in AP and a-g1-g2-g3-g2n-b are in GP and h is the harmonic mean of a and b then a1-a2n-g1g2n-a2-a2n-1-g2g2n-1-an-an-1-gngn-1 is equal to

The correct option is D 2n/h a _ 1 + a _ 2n / g _ 1 g _ 2n + a _ 2 + a _ 2n 1 / g _ 2 g _ 2n 1 +........+ a _ n + a _ n+1 / g _ n g _ n+1 =n( 2 ...

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Dimensional Analysis

If a,a1,a2,...

Question

If $a, a_{1}, a_{2}, a_{3}, . . . ., a_{2 n}, b$ are in AP and $a, g_{1}, g_{2}, g_{3}, . . . ., g_{2 n}, b$ are in GP and h is the harmonic mean of a and b then $\frac{a_{1} + a_{2 n}}{g_{1} g_{2 n}} + \frac{a_{2} + a_{2 n - 1}}{g_{2} g_{2 n - 1}} + . . . . + \frac{a_{n} + a_{n + 1}}{g_{n} g_{n + 1}}$ is equal to

\frac{2 n}{h}

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2nh

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\frac{n}{h}

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Similar questions

a, a_{1}, a_{2}, a_{3}, a_{4}, . . . . . ., a_{2 n}, b

a, g_{1}, g_{2}, g_{3}, g_{4}, . . . . . . . ., g_{2 n}, b

h

a

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\frac{a_{1} + a_{2 n}}{g_{1} g_{2 n}} + \frac{a_{2} + a_{2 n - 1}}{g_{2} g_{2 n - 1}} + . . . . + \frac{a_{n} + a_{n + 1}}{g_{n} g_{n + 1}}

a, a_{1}, a_{2}, . . . . ., a_{2 n}, b

a, g_{1}, g_{2}, . . . . g_{2 n}, b

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\frac{a_{1} + a_{2 n}}{g_{1} g_{2 n}} + \frac{a_{2} + a_{2 n - 1}}{g_{2} g_{2 n - 1}} + . . . . . + \frac{a_{n} + a_{n + 1}}{g_{n} g_{n + 1}}

a, a_{1}, a_{2}, . . . . . a_{2 n}, b

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

a_{r} > 0, r ϵ N

a_{1}

a_{2}

a_{3}

a_{2 n}

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

a_{r} > 0, r \in N

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

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

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