Binomial theorem for any index:

(1+x)ⁿ = 1+ nx +

 Observations: 

• Expansion is valid only when -1 <x <1
• General part of the series (1+x)^-n = T_r+1 = (-1)^r   x^r
• General part of the series (1-x)^-n = T_r+1 =   x^r
• If first term is not 1, then create first term unity in the given way:

             (a+ x)ⁿ = aⁿ(1+x/a)ⁿ  if < 1     

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