#1714 · Real Analysis · Series

Convergence of a squared-term series

Determine the values of $x$ for which the following series is convergent or divergent: $\frac{1 ^{2}}{2 ^{2}} + \frac{1 ^{2} \cdot 3 ^{2}}{2 ^{2} \cdot 4 ^{2}} x + \frac{1 ^{2} \cdot 3 ^{2} \cdot 5 ^{2}}{2 ^{2} \cdot 4 ^{2} \cdot 6 ^{2}} x^{2} + \dots$

~10 minProof · checked by AIRatio testPower seriesGauss's test

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. XXI. Convergency and Divergency of Series, Examples XXI.b, No. 6

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