Binomial theprem and expansion

AI Thread Summary
The discussion focuses on the expansion of the binomial expression (1+x)^n, specifically seeking the last few terms of the series. The final terms are identified as n(n-1)x^(n-2)/2!, nx^(n-1)/1!, and x^n. Additionally, there is a query about proving the inequality (1+n)^n ≥ 5/2n^n - 1/2n^(n-1), with a request for guidance on the proof. The thread concludes with a note that it was also categorized under "homework," leading to its closure. The exchange emphasizes understanding binomial coefficients and their properties.
rohan03
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(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 textbook answer for this.
 
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hi rohan03! :smile:

(try using the X2 and X2 buttons just above the Reply box :wink:)

the binomial coefficients are symmetric (nCr = nCn-r),

so it ends … + n(n-1) xn-2/2! + nxn-1/1! + xn :wink:
 
Thank you . Can I prove with the help of this :
(1+n)n ≥ 5/2nn- 1/2n n-1
 
and if yes - please guide on how
 
rohan03 said:
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? :smile:
 
This was also posted under "homework" so I am closing this thread.
 
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