#1901 · Algebra · Sequences & series

Sum of binomial series coefficients

Prove that, if $n$ be a positive integer, $1 - 3 n + \frac{3 n ( 3 n - 3 )}{1 \cdot 2} - \frac{3 n ( 3 n - 4 ) ( 3 n - 5 )}{1 \cdot 2 \cdot 3} + \dots = 2 (- 1)^{n}$ .

~20 minProof · checked by AIBinomial theoremSeries summation

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Miscellaneous Examples, No. 296

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.