r(r -- 1){r .3 3! where r is an arbitrary integral or fractional exponent. The necessary condition |x|

Number 8b

$r(r -- 1){r .3 3! where r is an arbitrary integral or fractional exponent. The necessary condition |x| < 1 for convergence was not stated by Newton. 8. Use the binomial theorem to obtain the following series expansions. – x³ + · . . (1+x)-1 = 1 – x +x? (a) + (-1)$

Extracted text: r(r -- 1){r .3 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.="" –="" x³="" +="" ·="" .="" .="" (1+x)-1="1" –="" x="" +x?="" (a)="" +="" (-1)"x"="" +="" ·...="" (1–="" x)-2="1+" 2x="" +="" 3x²="" +="" .="" (b)="" %3d="" +="" (n="" +="" 1)x"="" +.="">

Jun 05, 2022

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r(r -- 1){r .3 3! where r is an arbitrary integral or fractional exponent. The necessary condition |x|

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