#1490 · Algebra · Sequences & series
Binomial Series Identity Transformation
Prove that $1 + rac{2n}{3} + rac{2n(2n+2)}{3 imes 6} + rac{2n(2n+2)(2n+4)}{3 imes 6 imes 9} + its = 2^n
ewlines imes \{ 1 + rac{n}{3} + rac{n(n+1)}{3 imes 6} + rac{n(n+1)(n+2)}{3 imes 6 imes 9} + its \}$.
H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. XIV. Binomial Theorem: Any Index, Examples XIV.c, No. 7
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