#1044 · Algebra · Sequences & series

Limit of a geometric term

If $r < 1$ and positive, and $m$ is a positive integer, shew that $(2 m + 1) r^{m} (1 - r) < 1 - r^{2 m + 1}$ . Hence shew that $n r^{m}$ is indefinitely small when $n$ is indefinitely great.

~15 minProof · checked by AIinequalitieslimitsgeometric progression

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. V. Geometrical Progression, Examples V.b, No. 23

Stuck? A gentle nudge

Something off?

Workspace

Your working

Check your full solution

Attach photos of your pages (up to 3) or one PDF — or check what you typed above. Lemma reads the work and verifies the reasoning, not just the answer.

Your first check today doesn't need an account.

Your photos and PDFs are read once and not stored — only the transcription is kept.