# Math Help - Can the series (k!)/(1x2x3...(2k-1)) be written as the series (k!)/(2k-1)!?

1. ## Can the series (k!)/(1x2x3...(2k-1)) be written as the series (k!)/(2k-1)!?

It was a question on one of my exams and I think my TA graded it wrongly because he wrote that:

$\sum \frac {k!}{1x2x3...(2k-1)} = \sum \frac {k!}{(2k-1)!}$

I disagree, but can someone explain it?

2. Originally Posted by chrozer
It was a question on one of my exams and I think my TA graded it wrongly because he wrote that:

$\sum \frac {k!}{1x2x3...(2k-1)} = \sum \frac {k!}{(2k-1)!}$

I disagree, but can someone explain it?
I assume those x's refer to multiplication?

Well it seems as if you're multiplying consecutive integers in that denominator, and by definition $n!=n(n-1)(n-2)\cdots 3\cdot 2\cdot 1$. Thus, we can say that $1\cdot2\cdot3\cdots(2k-1)=(2k-1)!$.

Does this clarify things?

3. Yes it does. Thanks alot. I had it confused with something else.