Important Equations

Binomial Expansion

For any value of n, whether positive, negative, integer or non-integer, the value of the nth power of a binomial is given by:
 
 
 In many derivation we are using Binomial expansion to simplify the expression or formula.
 
Important Expansion
1/(1-x)=1+x+x^2+x^3+x^4+x^5+... for -1<x<1  
e^x=1+x+1/2x^2+1/6x^3+1/(24)x^4+... for -infty<x<infty  
ln(1+x)=x-1/2x^2+1/3x^3-1/4x^4+... for -1<x<1  
 
Summation
 
Sum of first N numbers = n(n+1)/2
Sum of squares of N numbers = n(n+1)(2n+1)/6

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