#1707 · Real Analysis · Series

Finiteness of an infinite product

Show that the infinite product $\frac{2}{1} \cdot \frac{2}{3} \cdot \frac{4}{3} \cdot \frac{4}{5} \cdot \frac{6}{5} \dots \frac{2 n - 2}{2 n - 3} \cdot \frac{2 n - 2}{2 n - 1} \cdot \frac{2 n}{2 n - 1}$ is finite when $n$ is infinite.

~15 minProof · checked by AIinfinite productsconvergency

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. XXI. Convergency and Divergency of Series, Examples XXI.a, No. 21

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