Binomial theprem and expansion

[rohan03]

Main Question or Discussion Point

(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.

 

[tiny-tim]

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 ​

 

[rohan03]

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

 

[rohan03]

and if yes - please guide on how

 

[tiny-tim]

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

just write out the last three terms …

what do you get? ​

 

[HallsofIvy]

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