#1488 · Algebra · Sequences & series

Prove an infinite series identity

Prove that $1 - \frac{1}{2} \cdot \frac{1}{2} + \frac{1 \cdot 3}{2 \cdot 4} \cdot \frac{1}{2 ^{2}} - \frac{1 \cdot 3 \cdot 5}{2 \cdot 4 \cdot 6} \cdot \frac{1}{2 ^{3}} + \frac{1 \cdot 3 \cdot 5 \cdot 7}{2 \cdot 4 \cdot 6 \cdot 8} \cdot \frac{1}{2 ^{4}} - \dots = \frac{2}{3}$ .

~10 minProof · checked by AIbinomial theoremseries summation

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. XIV. Binomial Theorem: Any Index, Examples XIV.c, No. 5

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.