ZOJ Problem Set - 2949
Luck is the key to life. When I have to decide something, I will make my decision by flipping a coin. And then, I have two things to do. First, I have the decision made. Second, I go to the nearest church and donate the coin.
But there are always too many things I have to decide. For example, what should I eat today for lunch? OK, now we are talking about a decision, so let us assume that I have two kinds of food: quick-served noodle A and quick-served noodle B.
I just have bought N bowls of noodle A and N bowls of noodle B. If I have some space to make a decision (i.e. having two kinds of quick-served noodle to choose from), then I will flip a coin to decide which kind of noodle to eat.
My question is, before I eat up all 2 * N bowls of quick-served noodle, what is the mathematical expectation of the number of coins I will have to donate.
Standard input will contain multiple test cases. The first line of the input is a single integer T (1 <= T <= 1000) which is the number of test cases. And it will be followed by T consecutive test cases.
Each test case contains an integer N (1 <= N <= 1000).
OutputResults should be directed to standard output. The output of each test case should be a single real number, which is the mathematical expectation of the number of coins I have to donate. The result should be accurate to two digits after the fractional point.
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Author: CHEN, Zhengguang
Source: Zhejiang University Local Contest 2008