#1479 · Algebra · Sequences & series

Coefficient in Negative Power Expansion

Prove that the coefficient of $x^{r}$ in the expansion of $(1 - 4 x)^{- \frac{1}{2}}$ is $\frac{( 2 r )!}{( r ! ) ^{2}}$ .

~10 minProof · checked by AIBinomial TheoremCombinatorics

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. XIV. Binomial Theorem: Any Index, Examples XIV.b, No. 33

Stuck? A gentle nudge

Something off?

Workspace

Your working

Check your full solution

Upload photos of your handwritten work or a PDF, and Lemma will read it and tell you whether it's right — and where it first goes wrong if not.