familiar form r (r – 1) (1+x)" = 1+rx + 2! r(r – 1)(r – 2) x³ + · · , 3! where r is an arbitrary integral or fractional exponent. The necessary condition |x|

Number 8a

Extracted text: familiar form r (r – 1) (1+x)" = 1+rx + 2! r(r – 1)(r – 2) x³ + · · , 3! where r is an arbitrary integral or fractional exponent. The necessary condition |x| < 1="" for="" convergence="" was="" not="" stated="" by="" newton.="" 8.="" use="" the="" binomial="" theorem="" to="" obtain="" the="" following="" series="" expansions.="" (1+x)-l="1" –="" x="" +="" x²="" –="" x³="" +="" ·="" ..="" (a)="" %3d="" +(-1)"x"="" +="" ·="" ...="" (1="" –="" x)-2="1+" 2x="" +="" 3x²="" +="" .="" .="" (b)="" %3d="" +="" (n="" +="" 1)x"="">