#1701 · Real Analysis · Series

Power series with rational coefficient

Determine whether the series $x + \frac{3}{5} x^{2} + \frac{8}{10} x^{3} + \frac{15}{17} x^{4} + \dots + \frac{n ^{2} - 1}{n ^{2} + 1} x^{n} + \dots$ is convergent or divergent for $x > 0$ .

~8 minProof · checked by AIpower seriesratio test

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. XXI. Convergency and Divergency of Series, Examples XXI.a, No. 11

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.