Find the value of a 1 a 1 -1- a 2 a 2 -1- a 3 a 3 -1- - - a 1 - a 2 - a 3 - being positive and greater than unity-

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Summation by Sigma Method

Find the valu...

Question

Find the value of $\frac{a_{1}}{a_{1} + 1 -} \frac{a_{2}}{a_{2} + 1 -} \frac{a_{3}}{a_{3} + 1 -} \dots, a_{1}, a_{2}, a_{3}, \dots$ being positive and greater than unity.

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

(a_{1} + a_{2} + a_{3} + . . . . . . . + a_{n}) (\frac{1}{a_{1}} + \frac{1}{a_{2}} + \frac{1}{a_{3}} . . . . . . . . . . . . + \frac{1}{a_{n}}) \geq n^{2}

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

a_{1}, a_{2}, a_{3} . . . . a_{n} \in R^{+}

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

(1 + a_{1} + a_{1}^{2}) (1 + a_{2} + a_{2}^{2}) (1 + a_{3} + a_{3}^{2}) . . . . (1 + a_{n} + a_{n}^{2})

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}}

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