Intereting Posts

Is $\sqrt{x^2}$ always $\pm x?$
Characterization of irreducible elements in integral domains.
If $\sin A+\sin B+\sin C=\cos A+\cos B+\cos C=0$, prove that:…
Variable leaving basis in linear programming – when does it happen?
Expected value of the number of flips until the first head
Prove that $n\choose0$+$n+1\choose1$+$n+2\choose2$+…+$n+m\choose{m}$=$n+m+1\choose{m}$ combinatorically
Number of permutations that strictly contain two consecutive vowels
Dependence of the Sobolev embedding constants on the domain
Fundamental group of two tori with a circle ($S^1✕${$x_0$}) identified
Schwarz's lemma $\Rightarrow$ an analytic conformal map UHP$\to$UHP must be an FLT?
Find the value of : $\lim_{n\to\infty}(2a)^{\frac{n}{2}}\sqrt{a-\sqrt{a(a-1)+\sqrt{a(a-1)+\cdots}}}$
Characterizing bell-shaped curves
Irreducibility of $x^{n}+x+1$
$\sqrt{x}$ isn't Lipschitz function
Number theoretic proof that $n\mid\phi(a^n-1)$

$\left(\forall n \in \mathbb{N}\right)\left((n + 1)! = (n + 1) \cdot n!\right)$

Prove the following statement by induction: for all $n \in \mathbb{N}$

$\sum_{k=0}^{n}(k \cdot k!) = (n + 1)! − 1$

- Translating English into First Order Logic
- What is the history of this theorem about the finite sum of a polynomial?
- Help with a recurrence with even and odd terms
- Prove or disprove statements about the greatest common divisor
- Number of combinations such that each pair of combinations has at most x elements in common?
- $x_1+x_2+\cdots+x_n\leq M$: Cardinality of Solution Set is $C(M+n, n)$

Base case: $n =0$

$(0\cdot 0!) = 0 ~\wedge~ (0+1)! – 1 = 0$, true.

Assume $n$ is true so $k = n+1$

$(n+1)\cdot(n+1)!= (n+1)\cdot(n+1)n!$

I’m not sure where to carry on from here? Can anyone shed some light?

- Recursion: putting people into groups of 1 or 2
- Decomposing a discrete signal into a sum of rectangle functions
- Relationship Between The Z-Transform And The Laplace Transform
- Prove this recurrence relation? (catalan numbers)
- Proving any product of four consecutive integers is one less than a perfect square
- Is this reflexive?
- Ways to have exactly $n$ nominees out of $2n$ voters
- strong induction postage question
- How many distinct ways to climb stairs in 1 or 2 steps at a time?
- At least one monochromatic triangle from $p_n=\lfloor{en!}\rfloor+1$ points

$$\sum_{k=0}^{n+1} k{\cdot}k!=\sum_{k=0}^nk{\cdot}k!+(n{+}1){\cdot}(n{+}1)!=(n{+}1)!{-}1+(n{+}1){\cdot}(n{+}1)!=(n{+}2){\cdot}(n{+}1)!{-}1=(n{+}2)!{-}1$$

@ASoni Yes,

(n+1)!−1+(n+1)⋅(n+1)!=(n+1)!+(n+1)⋅(n+1)!−1=(n+1)!(1+n+1)−1(n+1)!−1+(n+1)⋅(n+1)!=(n+1)!+(n+1)⋅(n+1)!−1=(n+1)!(1+n+1)−1

– user2345215 Nov 11 ’14 at 22:56

How do you get from `(n+1)!+(n+1)⋅(n+1)!−1`

to `(n+1)!⋅(1+n+1)−1`

?

Factoring out `(n+1)!`

from `(n+1)!+[(n+1)⋅(n+1)!]−1`

you will have `(n+1)!⋅[1+(n+1)]-1`

.

Similarly, you may wish to factor a `2`

out of only the first two of three terms in `(2+4)-1`

. In which case you will have `[2⋅(1+2)]-1`

.

- Why is this polynomial irreducible?
- $^{\mathbb{N}}$ with respect to the box topology is not compact
- On the norm of a quotient of a Banach space.
- Integral $\int_0^{1/2}\arcsin x\cdot\ln^2x\,dx$
- Shortest Path with odd number of “Green” vertices
- On the generating function of the Fibonacci numbers
- Are injectivity and surjectivity dual?
- Small perturbation of linear transformation cannot decrease its rank
- What is the difference between probability and statistics?
- half space is not homeomorphic to euclidean space
- The concept of random variable
- Finitely generated integral domain and finitely generated $k$-algebra.
- What is “ultrafinitism” and why do people believe it?
- Ackermann Function primitive recursive
- Non-revealing maximum