EasySequences & series

#1052 · Algebra · Sequences & series

Harmonic Mean Relation

If $b$ is the harmonic mean between $a$ and $c$ , prove that $rac{1}{b-a} + rac{1}{b-c} = rac{1}{a} + rac{1}{c}$ .

~8 minProof · checked by AIharmonic meanalgebraic manipulation

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. VI. Harmonical Progression, Examples VI.a, No. 9

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.