# what is the expansion of ( 1 + x)1/x.

SAGAR SINGH - IIT DELHI
879 Points
12 years ago

Dear eshita,

A variant of the binomial formula is obtained by substituting 1 for x and x for y, so that it involves only a single variable. In this form, the formula reads

$(1+x)^n = {n \choose 0}x^0 + {n \choose 1}x^1 + {n \choose 2}x^2 + \cdots + {n \choose {n-1}}x^{n-1} + {n \choose n}x^n,$

or equivalently

$(1+x)^n = \sum_{k=0}^n {n \choose k}x^k.$

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All the best.