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### What is the term for a factorial type operation, but with summation instead of products? [duplicate]

(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 ...
109k views

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### What must be the simplest proof of the sum of first $n$ natural numbers? [duplicate]

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.
11k views

### Proving the sum of the first $n$ natural numbers by induction [duplicate]

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 ...
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### Using Direct Proof. $1+2+3+\ldots+n = \frac{n(n + 1)}{2}$ [duplicate]

I need help proving this statement. Any help would be great!
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### Can you explain this please $T(n) = (n-1)+(n-2)+…1= \frac{(n-1)n}{2}$ [duplicate]

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 ...
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### Why does $1+2+\dots+2003=\dfrac{2004\cdot2003}2$? [duplicate]

Why does $1+2+\dots+2003=\dfrac{2004\cdot2003}2$? Sorry if this is missing context; not really much to add...
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### Find the sum $\sum_{j=0}^{n}j$ [duplicate]

Find the sum $\sum_{j=0}^{n}j$ for all $n=0,1,2,3,\dots$. How do I find/evaluate this sum?
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### How do I expand/solve the following summation? [duplicate]

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

### Evaluate the sum $1+2+3+…+n$ [duplicate]

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.
193 views

### How does this image prove the identity $1+2+3+4\cdots + (n-1) = \binom{n}{2}$? [duplicate]

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 ...
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### Why does $1+2+3+\cdots+p = {(1⁄2)}\cdots(p+1)$ [duplicate]

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 ...
### Why is $\sum\limits_{i=1}^n i = \frac{n(n+1)}{2}$? [duplicate]
Possible Duplicate: Proof for formula for sum of sequence $1+2+3+\ldots+n$? I was just messing around in Haskell: ...