It was a question on one of my exams and I think my TA graded it wrongly because he wrote that:
$\displaystyle \sum \frac {k!}{1x2x3...(2k-1)} = \sum \frac {k!}{(2k-1)!}$
I disagree, but can someone explain it?
It was a question on one of my exams and I think my TA graded it wrongly because he wrote that:
$\displaystyle \sum \frac {k!}{1x2x3...(2k-1)} = \sum \frac {k!}{(2k-1)!}$
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 $\displaystyle n!=n(n-1)(n-2)\cdots 3\cdot 2\cdot 1$. Thus, we can say that $\displaystyle 1\cdot2\cdot3\cdots(2k-1)=(2k-1)!$.
Does this clarify things?