2001 Putnam A2

You have coins $C_1,C_2,\ldots,C_n$. For each $k$, $C_k$ is biased so

that, when tossed, it has probability $1/(2k+1)$ of falling heads.

If the $n$ coins are tossed, what is the probability that the number of

heads is odd? Express the answer as a rational function of $n$.

您有硬币 $C_1,C_2,\ldots,C_n$。对于每个 $k$，$C_k$ 是有偏差的，因此

当抛掷时，它有 $1/(2k+1)$ 正面掉落的概率。

如果抛掷 $n$ 个硬币，则出现的概率是多少？

头很奇怪吗？将答案表示为 $n$ 的有理函数。