Prove a root series identity

Prove that $8 = 1 + \frac{3}{4} + \frac{3 \cdot 5}{4 \cdot 8} + \frac{3 \cdot 5 \cdot 7}{4 \cdot 8 \cdot 12} + \dots$ .

~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. 6

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