Using binomial theorem, evaluate ( 1.025) to the power of -1 / 3. Correct to four places of decimals?

The series which arises in the negative binomial theorem for negative integer -n(a+x)-n=k=0  Ck-n a-n-kxk =k=0  (-1)k×Ck n+k-1 a-n-kxk For a=1(1+x)-n=1-nx+12n(n+1)x2-16n(n+1)(n+2)x3+....Now(1.025)-13=(1+.025)-13(1+.025)-13=1-13×0.025 +12×13(13+1)(0.025)2-16×13(13+1)(13+2)(0.025)3Neglecting the higher terms(1+.025)-13=0.9918

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