Description of binomial expansion

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SUMMARY

The coefficient of x^n in the expansion of (1+x)^-1 is given by (-1)^n, while for (1-x)^-1, it is also (-1)^n. This follows from the application of the binomial expansion formula, specifically the generalized term tr = C(n,r) a^(n-r) x^r, where C(n,r) represents the binomial coefficient. The discussion highlights the importance of recognizing the appropriate signs in the coefficients when using the binomial expansion for negative exponents.

PREREQUISITES
  • Understanding of binomial expansion principles
  • Familiarity with binomial coefficients (C(n,r))
  • Knowledge of infinite geometric series
  • Basic algebraic manipulation skills
NEXT STEPS
  • Study the properties of binomial coefficients in depth
  • Learn about the convergence of infinite series
  • Explore advanced applications of binomial expansion in calculus
  • Investigate the relationship between binomial expansion and Taylor series
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Mathematicians, students studying algebra, educators teaching binomial expansion, and anyone interested in series and sequences in mathematics.

squids
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what will be the coefficient of the x^n in the expansion of (1+x)^-1 and(1-x)^-1. Please answer it separately..
 
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According to the spirit of this forum, an attempt on your part will help to encourage someone to help you.
 
i used the general term as tr=C(n,r) a^(n-r)*x^r. however i could not have a final answer as i supposed this method is not approate so there may be other wayz to solve. and using above formula i always got the answer without the appropriate sign..could anyone help for it..
 
You can use

(1 + x)^{m} = 1 + mx/(1!) + m(m - 1)x^{2}/(2!) + ...
 
ya i used it but what should be the nth term...i have no idea...pls give me some..
 
squids said:
what will be the coefficient of the x^n in the expansion of (1+x)^-1 and(1-x)^-1. Please answer it separately..

I am sure you have seen the answers to these questions, even before you ever heard of the binomial expansion!

RGV
 
I believe Ray Vickson is referring to the formula for the infinite geometric sum.
 

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