Central Binomial Series
Evaluate $\sum_{n=0}^{\infty} \binom{2n}{n} / 8^n = 1 + 2/8 + 6/64 + 20/512 + \dots$. Give an exact closed form such as sqrt(5); a decimal correct to three places is also accepted.
Related problems & prerequisites
Worth solving first
- The Other Pair of Dice 6.0/10
- Even Letters 6.0/10
- Every Third Binomial 6.0/10
Source: Classic generating-function identity in wide circulation; no traceable original source. Statement written for AxiomIQ.