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Let A=a1,a2,a...

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Let A={a1,a2,a3,a4}where a1>a2>a3>a4 The total no of unordered pairs of disjoint subsets of A is equal to

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a_{1}, a_{2}, a_{3}, a_{4}, a_{5} > 0

\frac{a_{1}}{a_{2} + a_{3}} + \frac{a_{2}}{a_{3} + a_{4}} + \frac{a_{3}}{a_{4} + a_{5}} + \frac{a_{4}}{a_{5} + a_{1}} + \frac{a_{5}}{a_{1} + a_{2}} \geq \frac{5}{2}

a_{1}, a_{2}, a_{3}, a_{4}

are in AP, then

\frac{1}{\sqrt{a_{1}} + \sqrt{a_{2}}} + \frac{1}{\sqrt{a_{2}} + \sqrt{a_{3}}} + \frac{1}{\sqrt{a_{3}} + \sqrt{a_{4}}}

a_{1}, a_{2}, a_{3}, a_{4}

are terms of an AP, then the relation between them is

a_{1}, a_{2}, a_{3}, a_{4}, . . {. ., a}_{20}

a_{1} + a_{20} = 45

a_{1} + a_{2} + a_{3} + a_{4}, . . {. . + a}_{20}

a_{1}, a_{2}, a_{3}, a_{4}

are the coeffecients of any four consecutive term in the expansion of

{(1 + x)}^{n}

\frac{a_{1}}{a_{1} {+ a}_{2}} + \frac{a_{3}}{a_{3} {+ a}_{4}}

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