1. Apr 1, 2012 #1

   rohan03

   

   (1+x)^n=1+nx/1!+(n(n-1) x^2)/2!+⋯+ what are the last few terms of this ? I looked and tried but don't seem to get any text book answer for this.

    

   rohan03, Apr 1, 2012
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3. Apr 1, 2012 #2

   tiny-tim

   

   Science Advisor

   Homework Helper

   hi rohan03!
   
   (try using the X² and X₂ buttons just above the Reply box )
   
   the binomial coefficients are symmetric (ⁿC_r = ⁿC_n-r),
   
   

   so it ends … + n(n-1) x^n-2/2! + nx^n-1/1! + xⁿ ​

    

   tiny-tim, Apr 1, 2012
4. Apr 1, 2012 #3

   rohan03

   

   Thank you . Can I prove with the help of this :
   (1+n)ⁿ ≥ 5/2nⁿ- 1/2n ^n-1

    

   rohan03, Apr 1, 2012
5. Apr 1, 2012 #4

   rohan03

   

   and if yes - please guide on how

    

   rohan03, Apr 1, 2012
6. Apr 1, 2012 #5

   tiny-tim

   

   Science Advisor

   Homework Helper

   just write out the last three terms …
   
   

   what do you get? ​

    

   tiny-tim, Apr 1, 2012
7. Apr 1, 2012 #6

   HallsofIvy

   

   Staff Emeritus

   Science Advisor

   This was also posted under "homework" so I am closing this thread.

    

   HallsofIvy, Apr 1, 2012

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