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  Quickly Revise - Exponential Series.....   Awaiting Review for Nickels
Tagged with:  self written     academic    [Post New]posted on 6 Dec 2007 21:47:39 IST    
Quickly Revise - Exponential Series...



  • ex = 1 + x + x2/2!  + x3/3! + .........infinity

  • e-x = 1 - x + x2/2!  - x3/3! + .........infinity

  • (ex + e-x ) = 2 ( 1 + x2/2!  + x4/4! + ........infinity )

  • (ex - e-x ) = 2 ( x + x3/3!  + x5/5! + ........infinity )

  • e = 1 + 1 + 1/2! + 1/3! + .........infinity
             =[ n][ infinity ] ( 1 + 1/n )n = [n=0 ][infinity] ( 1/n! )

  • e-1 =  1/2! - 1/3! + 1/4! - 1/5!.........infinity
             =[ n]lim[infinity] ( 1 - 1/n )n = [n=0 ]Sum[infinity] (-1)n( 1/n! )

  • e + e-1 = 2 ( 1 + 1/2! + 1/4! + 1/6! + .......infinity )

  • e - e-1 = 2 ( 1 + 1/3! + 1/5! + 1/7! + .......infinity )

  • [ n]lim[ infinity ] ( 1 (+-) 1/n )nx =e(+-)(x)  for all  x

  • [n=0 ]Sum[ infinity ] ( 1/n! )  =  [n=0 ]Sum[infinity ] ( 1/(n-1)! )  = [n=0 ]Sum[infinity ] ( 1/(n-2)! ) = e

  • [n=1]Sum[infinity] ( 1/n! )  = e - 1

  • [n=2]Sum[infinity] ( 1/n! )  = e - 2..........etc.



hope this will be helpful.........
 		About the Author:
Aatish (2303)

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Olaaa!! Perrrfect answer. 413  [532 rates]
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Aatish
Aatish is offline comment by Aatish    (posted on 6 Dec 2007 21:48:26 IST)
I am sorry for invisibility.......posting in the edited version soon.........
Mr.IITIAN007
Mr.IITIAN007 is offline comment by Mr.IITIAN007    (posted on 6 Dec 2007 22:22:00 IST)
cool concepts
Aatish
Aatish is offline comment by Aatish    (posted on 6 Dec 2007 22:26:22 IST)
pls comment NOW!!!!!
johri_anshuman
johri_anshuman is offline comment by johri_anshuman    (posted on 6 Dec 2007 22:29:31 IST)
nice....
mydarshankumar
mydarshankumar is offline comment by mydarshankumar    (posted on 6 Dec 2007 22:52:53 IST)
good.........
rosefantasy_dolly
rosefantasy_dolly is offline comment by rosefantasy_dolly    (posted on 7 Dec 2007 22:11:17 IST)
nice
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