Sequence Counting

Probability Level pending

How many strictly increasing finite sequences (having one or more terms) of positive integers less than or equal to 2017 with an odd number of terms are there?

\frac{4034!}{(2017!)^2}

2^{2018}-1

2^{2016}

2^{2017}-2017^2

1 solution

Jesse Li
Apr 22, 2019

There are 2017 numbers that could be in the sequence. Each number has 2 possibilities: it could either be in the sequence or not. Therefore, there are $2^{2017}$ sequences. Half of them have an even number of terms, so we need to divide by 2. $\frac{2^{2017}}{2}=\boxed{2^{2016}}$

Sequence Counting

1 solution

0 pending reports