A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 4 years ago
True or False & why?
(n+1)! = n!(n+1)
This question is relating to series.
anonymous
 4 years ago
True or False & why? (n+1)! = n!(n+1) This question is relating to series.

This Question is Closed

ParthKohli
 4 years ago
Best ResponseYou've already chosen the best response.2Woah. You confused on here?

ParthKohli
 4 years ago
Best ResponseYou've already chosen the best response.2\((n + 1)! = n! \times (n + 1)\)

ParthKohli
 4 years ago
Best ResponseYou've already chosen the best response.2That's an axiom, isn't it?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0n! is a factorial though, in this case n will be infinite. I don't know, I'm asking if it's an axiom lol

ParthKohli
 4 years ago
Best ResponseYou've already chosen the best response.2\( \color{Black}{\Rightarrow (4 + 1)! = 4! \times 5 = 1 \times 2 \times 3 \times 4 \times5 = 5!}\)

ParthKohli
 4 years ago
Best ResponseYou've already chosen the best response.2That is an axiom, and that's also a way people prove that \(0! = 1\). :)

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0I suppose that makes sense, it just seems odd to me

vishweshshrimali5
 4 years ago
Best ResponseYou've already chosen the best response.0\[n! = n (n1)(n2)...\] SO, \[(n+1)! = (n+1)n(n1)(n2)... = (n+1)n!\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0\[\sum_{n=1}^{\infty} n!(2x1)^n\] for example, is one of the easier ones

ParthKohli
 4 years ago
Best ResponseYou've already chosen the best response.2\(n! = n(n  1)(n  2) \cdots 1\) Correction* :)

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0At first I couldn't tell what they were doing to get rid of the n!'s on the ratio test

ParthKohli
 4 years ago
Best ResponseYou've already chosen the best response.2I believe that a factorial may be expressed as \(\prod\).

vishweshshrimali5
 4 years ago
Best ResponseYou've already chosen the best response.0\[THANKS\] @ParthKohli

ParthKohli
 4 years ago
Best ResponseYou've already chosen the best response.2\[\prod_{i = 1}^{n}i = n!\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0sometimes we take 0!=1 as a convention :)

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Alright so that's the trick, anything else I should know about factoring n! out?

vishweshshrimali5
 4 years ago
Best ResponseYou've already chosen the best response.0Well......... Nothing so important.

ParthKohli
 4 years ago
Best ResponseYou've already chosen the best response.2It's actually a simple fact.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Simple, but not intuitive at first glance, at least not to me

ParthKohli
 4 years ago
Best ResponseYou've already chosen the best response.2\( \color{Black}{\Rightarrow \Large {16! \over 8!} = {16 \times 15 \times 14 \times 13 \times 12 \times 11 \times 10 \times 9 \cancel{\times 8!} \over \cancel{8!}}}\)

ParthKohli
 4 years ago
Best ResponseYou've already chosen the best response.2Let's just express 3! in terms of 2!. \(3! = 3 \times 2 \times 1 = 3 \times (2 \times 1) = 3 \times 2!\)

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0a small execise : rewrite \[\frac{1.3.5.7.........(2n+1)}{2.4.6.8.............2n}\] using "!"

experimentX
 4 years ago
Best ResponseYou've already chosen the best response.1dw:1343146818151:dw

experimentX
 4 years ago
Best ResponseYou've already chosen the best response.1dw:1343146998874:dw

ParthKohli
 4 years ago
Best ResponseYou've already chosen the best response.2Woah! That's some hardcore Mathematics!

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Yeah I'm getting an interval of convergence of 0.5 < x < 0.5 And a radius of convergence of 0.5

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Would you agree with that @experimentX ? The limit for this series goes to infinity, it diverges.

experimentX
 4 years ago
Best ResponseYou've already chosen the best response.1wait .. something went wrong!!

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0I'm using the ratio test... I think that's what you did too *looks back at what your wrote*

ParthKohli
 4 years ago
Best ResponseYou've already chosen the best response.2What a change! \(\mathbf{Factorials \Longrightarrow Calculus}\)

experimentX
 4 years ago
Best ResponseYou've already chosen the best response.1well .. factorials are the basics!!

experimentX
 4 years ago
Best ResponseYou've already chosen the best response.1lol ... i did the opposite!!

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0\[\lim_{n \rightarrow \infty} \left \frac{a_{n+1}}{a_n} \right \] \[\lim_{n \rightarrow \infty} \left \frac{(n+1)!(2x1)^{n+1}}{n!(2x+1)^n} \right \]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Using the axiom Parth pointed out I can then cancel...

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0\[\lim_{n \rightarrow \infty} \left \frac{\cancel{n!}(n+1)(2x1)^{\cancel{n}+1}}{\cancel{n!}\cancel{(2x+1)^n}} \right = \infty\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Divergent by the Ratio Test @ParthKohli & @experimentX if 2x1 = 0 then x \(\neq\) 0.5 So the interval of convergence is only from 0.5 to 0.5, noninclusive

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0But the radius? 0.5? 0? o_O

ParthKohli
 4 years ago
Best ResponseYou've already chosen the best response.2Oh no! Not THAT type of limits!

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0PS: People please give @experimentX a medal...

experimentX
 4 years ago
Best ResponseYou've already chosen the best response.1dw:1343147306986:dw nvm .. i'm at 99, can't grow any further. i guess ratio test is bad test for this series!!

experimentX
 4 years ago
Best ResponseYou've already chosen the best response.1dw:1343147733699:dw

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Hold on ladies & gents, let me reask this specific problem as a new question, that way proper credit can be due and we're not all offtopic technically :D

experimentX
 4 years ago
Best ResponseYou've already chosen the best response.1no ... i enjoy weird problems!!
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.