Represent $50+49+48$ and so on to zero How do I mathematically represent the operation of adding $50$, for example, to continuous decrements by $1$ until we reach $0$ ? $50+49+48+47+\dots$ until we reach $0$. For example, how do I put this problem in a way that WolframAlpha would understand and solve?
 A: Mathematically, you could write that as $$\sum_{i=0}^{50} (n-i)$$
which is the same as $$\sum_{i=0}^{50} i$$
Wolfram Alpha understands quite a bit of mathematical terms, so you can simply search for
sum of i for i from 0 to 50

http://www.wolframalpha.com/input/?i=sum+of+i+for+i+from+0+to+50
A: Sum of first $n$ natural numbers is given by 
$$S_n=\frac {n (n+1)}{2}$$
Using this you can find your sum without any calculator...
A: In Wolfram|Alpha we can write:
$$\operatorname{sum}[\operatorname{i},\operatorname{i}=0..50]$$
giving $1275$.
A: A Wolframalpha syntaxis for $$\sum_{k=a}^b g(k)$$  is 
sum( g(k), k, a, b)

And it's even surprisingly versatile symbolically...
Your case is $a=0,\ b=50,\ g(k)=50-k$
Side note: There is a counterpart for $\int_a^b g(x)\,dx$
int(g(x), x, a, b)

A: In mathematical notation, this would be written as $\sum_{k=0}^{50}k$, but Wolfram|Alpha would rather see it as something like sum of k from 0 to 50, and they also have widgets. Of course, you would always use the formal method (the one on the first line) in a formal paper, proof, or even a forum like here, but if you are just wanting to calculate it, you could send it to Wolfram|Alpha in the form on the second line.
