Linked Questions

(Pardon if this seems a bit beginner, this is my first post in math - trying to improve my knowledge while tackling Project Euler problems) I'm aware of Sigma notation, but is there a function/name ...

Not exactly a duplicate since this is answering a specific instance popular in social media. You might have seen the viral posts about "save a penny a day for a year and make $667.95!" The ...

Possible Duplicate: Proof for formula for sum of sequence $1+2+3+\ldots+n$? Is there a shortcut method to working out the sum of n consecutive positive integers? Firstly, starting at $1 ... 1 + ...

I was studying sequence and series and used the formula many times $$1+2+3+\cdots +n=\frac{n(n+1)}{2}$$ I want its proof. Thanks for any help.

I am currently studying proving by induction but I am faced with a problem. I need to solve by induction the following question. $$1+2+3+\ldots+n=\frac{1}{2}n(n+1)$$ for all $n > 1$. Any ...

I need help proving this statement. Any help would be great!

Possible Duplicate: Proof for formula for sum of sequence 1+2+3+…+n? Can you explain this please $$T(n) = (n-1)+(n-2)+…1= \frac{(n-1)n}{2}$$ I am really bad at maths but need to ...

We know that Gauss has shown that the sum $S$ of the first $n$ natural numbers is given by the relation: $$S=\frac{n(n+1)}{2} \tag{*}$$ The proof that I remember most frequently is as follows: Let ...

Why does $1+2+\dots+2003=\dfrac{2004\cdot2003}2$? Sorry if this is missing context; not really much to add...

Find the sum $\sum_{j=0}^{n}j$ for all $n=0,1,2,3,\dots$. How do I find/evaluate this sum?

$\sum\limits_{i=1}^{n-1} i$. I know the answer is $\frac{1}{2}(n-1)n$ but I don't quite understand it how to get there.

How do we evaluate the sum: \begin{equation*} 1+2+...+n \end{equation*} I don't need the proof with the mathematical induction, but the technique to evaluate this series.

Possible Duplicate: Proof for formula for sum of sequence 1+2+3+…+n? Proof without words: $\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad $ How does ...

Prove that the $n$-th triangular number is: $$T_n = \dfrac{n(n+1)}{2}$$ I did this: Base case: $\frac{1(1+1)}{2}=1$, which is true. Then I assumed that $T_k=\frac{k(k+1)}{2}$ is true. $$T_{k+...

I saw this from Project Euler, problem #1: If we now also note that $ 1+2+3+\cdots+p = {(1/2)} \cdot p\cdot(p+1) $ What is the intuitive explanation for this? How would I go about deriving the ...