If alpha -5 -2 - - 3-5 - 7 -3 - - 3- 2-5 - 7 - 9 -4 - - 3- 3- then alpha -4 - alpha -A 21B 23C 25D 27

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Summation by Sigma Method

if alpha =5 /...

Question

if alpha = 5/(2!×3) + (5×7)/(3!×3^2) + (5×7×9)/(4!×3^3) + ............, then alpha^2 + 4×alpha =

A) 21 B) 23 C) 25 D) 27

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If $α a n d β$ are the roots of the equation $4 x^{2} + 3 x + 7 = 0$ , then $\frac{1}{α} + \frac{1}{β} =$

I f a v a r i a b l e t a k e s t h e d i s c r e t e v a l u e s α + 4, α - \frac{7}{2}, α - \frac{5}{2}, α - 3, α - 2, α + \frac{1}{2}, α - \frac{1}{2}, α + 5 (α > 0), t h e n t h e m e d i a n i s :

α + 4, α - \frac{7}{2}, α - \frac{5}{2}, α - 3, α - 2 α + \frac{1}{2}, α - \frac{1}{2}, α + 5 (α > 0),

\tan^{- 1} (\tan \frac{5 π}{4}) and β = \tan^{- 1} (- \tan \frac{2 π}{3})

\frac{7 π}{12}

α = \frac{5}{2! 3} + \frac{5.7}{3! 3^{2}} + \frac{5.7.9}{4! 3^{3}}

α^{2} + 4 α

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