Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I have a small comprehension gap with an easy equation. I have following term and I don’t know how to multiply it correctly. $ (n+1)(n+1)!+(n+1)!-1 $

One intermediate step must be. $ (n+2)(n+1)!-1 $

The result should be $ (n+2)!-1 $.

How do I multiply the term correct? Is the attempt correct to multiply binomial series to $ (n+1)^2n!+(n+1)!-1 $?

It would awesome, if someone could help me.

share|cite|improve this question
up vote 17 down vote accepted

$$(n+1)\color{red}{(n+1)!}+\color{red}{(n+1)!}-1$$ $$=(n+1)![(n+1)+1]-1$$ $$=(n+2)(n+1)!-1$$ $$=(n+2)!-1$$

share|cite|improve this answer
First you add $ (n+1)!+(n+1)! $ together? – hofmeister Jan 23 '12 at 14:41
@Taz: No, I factored $(n+1)!$ first, which is common as I showed with red. What remains from first statement is $(n+1)$ and $1$ from the second one, which will be $(n+2)$. Multiplying $(n+2)$ and $(n+1)!$, we get $(n+2)!$. I hope it's clear now. – Gigili Jan 23 '12 at 15:13
Thanks now i got it! – hofmeister Jan 23 '12 at 15:24
Hope you don't mind my formatting. – Rasmus Jan 23 '12 at 15:27
Where are you? +1 – Babak S. Nov 26 '12 at 15:14

You would have no trouble with $(5)(n+1)!+(7)(n+1)!=(12)(n+1)!$ ($5$ apples plus $7$ apples equals $12$ apples.)

Maybe you would have a little trouble with $(5)(n+1)!+(n+1)!$, but not if you rewrite it as $(5)(n+1)! +(1)(n+1)!$ ($5$ apples plus $1$ apple equals $6$ apples).

Now let's look at $(n+1)(n+1)! +(n+1)!$. Rewrite this as $(n+1)(n+1)! +(1)(n+1)!$. We have $n+1$ apples plus $1$ apple is $n+2$ apples, so the sum is $(n+2)(n+1)!$, which can be rewritten as $(n+2)!$.

share|cite|improve this answer
+1 for two reasons: absurdly and casually turning the factorial into an apple (there is academic merit in that) and the coincidence I'm eating two apples. – 000 May 19 '12 at 6:30

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

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