# Why does Solve work on a sum with 34 terms but not 35 terms?

Posted 6 years ago
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 Why does this work when M=34 but not when M=35?:Clear [n, M, confidence, k, p]; n = 8; M = 34; confidence = 0.5; $\text{Solve}\left[\sum _{k=n+1}^M \frac{M! p^k (1-p)^{M-k}}{(M-k)! k!}=\text{confidence},p,\mathbb{R}\right]$
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Posted 6 years ago
 This code works on my system: With[{M = 35, n = 8, c = 1/2}, Solve[Sum[(M! p^k (1 - p^(M - k)))/((M - k)! k!), {k, n + 1, M}] == c, p, Reals]]