IIT JEE , AIEEE Forum - Mathematics , Algebra

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HERE IS THE PROOF...................

y = 3/4 + ( 3.5 )/ ( 16 . 2! ) + ( 3.5.7 )/ ( 64 .3! )
+ ( 3.5.7.9 )/( 256 . 4! ).........

THEREFORE ,

y + 1 = 1 + ( the above expression )

= 1 + 3/4 + (3.5 )/ (4.8) + ( 3.5.7 )/ (4.8.12 ) + .............

( rearrangement of factorial has been done )

= ( 1 - 1/2 ) ^ ( -3/2 )..........binomial expansion

squaring.........

(y + 1 )^ 2 = 8

=> y^2 +2y - 7 = 0

=> y = sqrt (8) -1

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