Factorials Definition and 91 Threads

I would like some direction on studying powers of integers and if they are in any way related to factorials. I was studying the sequence of cubics 1, 8, 27, 64, 125 and so. After a certain number of rounds of a basic rule I choose to apply to this sequence, I arrived at a new sequence...

How would you simplify (2n+1)! Is the same as (2n-1)! ?

In my combinatorics book, it's discussing inclusion-exclusion, and it says that n!-(n-1)! = (n-1)!*(n-1)! Can someone help me understand the rules of factorials? Thanks!

Homework Statement For some natural N the no of positive integers x satisfying the equation 1! + 2! + 3! + ... + x! = (N)2 is: A)one B)two C)infinite D)none The Attempt at a Solution I have no idea of how to start.. never came across such problems. By trial i have got two values...

Hi all. Does anybody know their stuff when it comes to math? More specifically calculating probability... i have a question about factorials and when they should be used. If you have let's say 2 events, the chance of event A is 1/2 the chance of event B is 1/3 you're just supposed to...

Is there a name and/or proof for the following conjecture? "For any prime p, p! is congruent to p2-p modulo p2." Thanks much.

I am unsure as to how factorials should be expanded. I have \sum\stackrel{1}{(2n!)} (if what was just typed did not make sense due to html error on my part, it is supposed to say the sum of 1/(2n)!) from n=1 to infinity. I did the ratio test and found the limit to be 0, which is less than...

I need to figure out the following factorial \frac{297!}{98! * 199!} then take the logarithim of that Is there a rule that I can use to simplify the equation and get the same result? , I did another example where I used \frac{310!}{2!*299!} and I figured it out to be...

Anyone know of any method to evaluate this limit, \lim_{n \to \infty} \frac{n!}{\left(\frac{n+p}{2}\right)!\left(\frac{n-p}{2}\right)!}2^{-n} it seems to go to zero, but I have no way to be sure.

Homework Statement Show that \sum \frac{n!}{10^n} converges or diverges.(Note, I was unsure of how to format this via latex, so the summation is from n = 1 to infinity.)Homework Equations The root test: |\frac{a_n_+_1}{a_n}| The Attempt at a Solution a_n=\frac{n!}{10^n}...

The problem at hand: \inline{\sum_{k=1}^n \frac{(k+1)!}{(k+3)!}} Hence, find the limiting sum of the series, as n ---> infinity. Start this summation by expanding out the factorial to have a common factor of k!(k+1) as follows: \sum_{k=1}^n \frac{(k+1)!}{(k+3)!} = \sum_{k=1}^n...

Homework Statement Find the lim as n-->inf of the sequence {an}= 1x3x5x...x(2n-1) _______________ n! Homework Equations The Attempt at a Solution I rewrote it as ...(2n-3)(2n-2)(2n-1) __________________ n(n-1)(n-2)...2x1 which leads me to believe that is...

Homework Statement Part of a much bigger problem, but I am hung up on solving the following: ln\left [ \left(\frac{N+n}{2}\right ) ! \right ] = \left ( \frac{N+n+1}{2}\right) \frac{ln(N+n)}{2}\right ) I am trying to follow a proof in...

I was reading and came across this statement: If t > 2n^2 is an integer, then t! > (n^2)^(t-n^2) I'm not sure why it is true. I don't know what equations are relevant. My feeling is that you don't need anything more than algebra, but perhaps it would also follow from the gamma function...

Homework Statement Hi! I need to find ratio (2n+1)!/(2n+3)! for interval of convergence calculation. Homework Equations 5! = 1*2*3*4*5The Attempt at a Solution i have no idea where to start since i have never dealt with factorials before.. if you just show me some kind off factorial...

Homework Statement I am confused about how to find a sum of a power series, especially when it contains factorials and I can't quite get it to look like a geometric series. Is it the same thing as finding a limit (and then I would follow the various tests for convergence of the different...

Homework Statement Determine whether the series converges or diverges. \sum\frac{37}{n!} I will just forget about the 37, and think of it as \sum\frac{1}{n!} I can try to decompose the n! n! = n(n-1)! n! = n ( n-1) (n-2)! n! = n(n-1)(n-2)(n-3)...2*1 so \sum\frac{1}{n!}...

Homework Statement Show that the definite integral from 0 to 1 (ln x)^n dx = n!(-1)^n Homework Equations The Attempt at a Solution i tried to integrate by parts and kept going on and on but i don't know how to incorporate the factorial in the answer ...

Hi, I was just looking at this problem with sequences and I was having a question about factorials. I understand that the factorials need to get smaller. I was just wondering what is the (3)(2)(1) in the problem symbolizing? Just that it will eventually reach the end? and what numbers...

Homework Statement This isn't a specific problem rather I don't know how to reduce factorials and this is giving me a hard time when I try the ratio test. For an example I'll use (2n+1)!/(2n+3)! Homework Equations The Attempt at a Solution I attempt it by writing out some...

hello everyone, I usually post my questions on one small czech mathematical forum, but here is an equation no one knows how to "solve". I`ve came to it by accident, when I made an mistake in one combinatorics equation. x! + (x-3)! = 16x - 24 its fairly simple to solve in one way(x has...

Homework Statement How is, [(N+Q)!Q!]/[(Q+1)!(N+Q-1)!] equal to (N+Q)/(Q+1) when N,Q>>1 ?? It looks like the Q!/(N+Q-1)! cancels but i don't see how, I am going from my lecturers notes here. Homework Equations The Attempt at a Solution

Hi I was trying to solve the equation (m + n)!/m! = v for "n" and found an online calculator http://www.hostsrv.com/webmab/app1/MSP/quickmath/02/pageGenerate?site=quickmath&s1=equations&s2=solve&s3=advanced#reply" which spit out the following as a solution: n = factorial(-1)[vm!] - m I...

I need to prove the following: n!/r! >= r^(n-r) With r and n as natural numbers and n>=r I know the LHS will end up being (n-r) terms long as the first r! will cancel out of n! (n>=r), but as they're both unknown, I just left it as 1*2*3*...*(n-2)*(n-1)*n 1*2*3*...*(r-2)*(r-1)*r and I looked...

Here is a sum from MATHCOUNTS: What are the last two digits in the sum of the factorials of the first 100 positive integers? From 1! to 4! you can add the units digits, since 5! to ... have 0 in their units place. From that I get 13, and I carry over the 1 over to the next column and...

Ok, so here goes nothing I have predict what this is in series form, the factorial in the numerator is really throwing me off. I only have to do the series for the first six terms. C0=C0 C2= -5/2 C0 C4= -3/4 C2 = (5x3)/(2x4) C0 C6= -1/6 C4 = -(5x3x1)/(2x4x6) C0 This is what I have so far...

can you please explain (step by step) how to factor the following: (n+1)! - 1 + (n+1)(n+1)! i have the answer, don't know how to get there!

I Have a small problem. I know the following: The series: S_{n} = 1 + 2 + 3 + 4 + 5 = \sum_{i=1}^{n=5}i 2S_{n} = 1 + 2 + 3 + 4 + 5 + 1 + 2 + 3 + 4 + 5 = n(n+1) = n^{2} + n Therefor: S_{n} = \frac{2S_{n}}{2} = \frac{n^{2} + n}{2} \sum_{i=1}^{n=5}i = \frac{n^{2} + n}{2} = \frac{25 +...

okay...I love math and i enjoy math a lot, mainly for its perfection and the aspect of not contradicting itself. But lately i have been runnig into contradictions and things that should not exist...and they piss me off. The worst of them is solving 0! 0!=1 why? i asked my math teacher...

The tex seems to be showing different problems than the ones I'm typing... maybe it's just me, but if what I'm talking about doesn't seem to make any sense, please quote my message to see what I've actually typed in the tex tags. If n is a positive integer and n > 1, prove that nC2 + (n-1)C2...

This is really a TeX/LaTeX question, but I wasn't sure where to put it. (Sorry!) I was looking at "Factoring Factorial n" (Guy, Amer. Math. Monthly Oct. '98) and became interested in looking at large factorials. Before I could really get started manipulating them I wanted a good way to store...

I need some general guidelines on how to simplify factorials. I'm in Calculus III and the Prof. and unfoutunately our textbook has glossed over how to do this. All the factorials we are dealing with now are in relation to sequences and series. so I'm dealing with expressions that...

Let u = 1 + \frac{x^{3}}{3!} + \frac{x^{6}}{6!} + \frac{x^{9}}{9!} + \dotsb v = x + \frac{x^{4}}{4!} + \frac{x^{7}}{7!} + \frac{x^{10}}{10!} + \dotsb w = \frac{x^{2}}{2!} + \frac{x^{5}}{5!} + \frac{x^{8}}{8!} + \dotsb Show that u^3 + v^3 + w^3 - 3 u v w = 1 Well, here...

The second part of this problem is giving me a hard time. I hope someone can help me with it: An airline pilot reported her itinerary for 7 days. She spent 1 day in Winnipeg, 1 day in Regina, 2 days in Edmonton, and 3 days in Yellowknife. a) how many different itineraries are possible...

I forgot most things about factorials but now I have to use them again to simplify expressions while doing convergence tests... What I know is: (n +1) ! = (n +1) n! (2n +1)! = (2n +1) 2n! ? but I don't know how to deal with these: (n -1) ! = ? (2n-1) ! = ? Thanks for any...

I was reading this tutorial and I came across this part which I didn't quite understand: I don't follow this. What does "a will be counted j times and will contribute i towards t" mean? Why does this show that t=s?

By definite integral, gamma function can be defined as \Gamma(z)= \int_{0}^{\infty} t^{z-1}e^{-t} dt I've learned some properties of Gamma function but my lecturer didn't tell us the domain of Gamma function. (I'm assuming it is defined for all non-negative real numbers). I thought of...

im dealing with a problem that isn't that hard, but its messing me up. its been a long time since i took high school and college math, but I am very smart. im trying to write an equation for the general description of a problem like this: you have a tile with x squares on it. you have a...

I wasn't really sure what forum this belonged in, but I'm doing an equation with Microsoft Excel, using Factorials. Basically, I'm wondering how you go about using them in an equation. Here's my current equation: =A5!/(A5-B5)!B5! Now obviously that comes back as an error. Does anyone have...

How would I go about simplifying something like: (n+3)!/(n+1)! ?

To calculate the multiplicities of 600 heads in 1000 coin tosses you start with 1000 choose 600 or 1000! / (600! * (1000-600)!) which equals 1000! / (600!) * (400!). Since you can't calculate this easily, apply Stirling's approx. N! = N^N * e^(-N) * sqrt(2piN). Applying this to...