I have a pretty simple straightforward question.

Q) Find the value of $x$ in the following: $$\frac{x}{10!} = \frac{1}{8!} + \frac{1}{9!}$$

Instinctively, I do the quickest thing I know how to do. $$\times10!\implies x = \frac{10!}{8!} + \frac{10!}{9!} = 9 \times 10 + 9 = 99$$ That seemed pretty easy and the back of my textbook says it's the right answer.

Just for fun, I do it again. Except this time, I initially multiply the equation with $9!$ instead of $10!$,

$$\times 9!\implies\frac{9!}{10!}x = \frac{9!}{8!} + \frac{9!}{9!}$$ $$\implies\frac{x}{10} = 9 + 1$$ $$\times 10\implies x = 10\times10 = 100$$ Sure, by multiplying by $10$ in the last step, I've still multiplied by $10!$.
But now, this $1\%$ variation in the answer has popped up.

So, I did what any highschooler would do in this situation;
I consulted Wolfram Alpha which told me that my $2^{\text{nd}}$ trial was correct.

Who should I believe? A computational knowledge engine or the back of my textbook?

  • 4
    $\begingroup$ $$\frac{(n+1)!}{n!}=n+1\;\ldots$$ $\endgroup$ – DonAntonio Mar 1 '14 at 17:42
  • 2
    $\begingroup$ Let me answer your question: you should believe your brain! $\endgroup$ – user63181 Mar 1 '14 at 17:42
  • $\begingroup$ @Sami: I never thought about that, but I will keep it mind. $\endgroup$ – Nick Mar 1 '14 at 18:02
  • 1
    $\begingroup$ @Don: Will recheck my calculations before I post questions again. Sir, yes, sir. $\endgroup$ – Nick Mar 1 '14 at 18:04
  • $\begingroup$ Lessons learnt: (1) I am an idiot who should find his brain and (2) do not doubt Wolfram's calculations. $\endgroup$ – Nick Mar 1 '14 at 18:09

There's a mistake in your first attempt:

$$ x = \frac{10!}{8!} + \frac{10!}{9!} = 10 \times 9 + 10 = 100 $$

  • $\begingroup$ hehe, omg, I can't believe i still make stupid mistakes like this. Thanks :D $\endgroup$ – Nick Mar 1 '14 at 17:40
  • 4
    $\begingroup$ Even the text book made it. So, it's not just you. :P $\endgroup$ – Priyatham Mar 1 '14 at 17:41
  • $\begingroup$ A better question would be what were the odds of that happening? $\endgroup$ – Nick Mar 1 '14 at 18:00
  • $\begingroup$ @Nick a question: did you look at the answer in the back of the book before or after you solved it? $\endgroup$ – Steven Stadnicki Jun 4 '14 at 1:24
  • 1
    $\begingroup$ @Steven: After.That was why it was so shocking. Now looking upon this silliness of the past version of myself, I feel like I ought to meditate more inorder to prevent my regression to idiocy. $\endgroup$ – Nick Jul 20 '14 at 7:46

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.