#1492 · Algebra · Sequences & series

Approximate Expansion of Function

Prove that approximately, when $x$ is very small, $\frac{3 ( x + \frac{4}{9} ) ^{\frac{1}{2}} ( 1 - \frac{3}{4} x ^{2} ) ^{\frac{1}{3}}}{2 ( 1 + \frac{9}{16} x ) ^{2}} = 1 - \frac{307}{256} x^{2}$ .

~15 minProof · checked by AIBinomial TheoremApproximations

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. XIV. Binomial Theorem: Any Index, Examples XIV.c, No. 9

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