Another proof without words!

These proof demonstrates the Gauss method to solve $1+2+3+4+...+100$ . The formula is $\frac{n\left(n+1\right)}{2}$ .

If you use this formula as a function, when $n$ is one of the natural numbers you get the Triangular Numbers.

It's very clear to figure out that these two portions individually expresses 1+2+3+4+5+6+7+8 which is a sum of algebraic expression with formula

$\boxed{n(n+1)/2}$

Concrete model is (8*9)/2, n=8, so .5(n)(n+1)

triangle problem and its answer 1/2(n+1)

It's nothing but a series of nth term natural number............1+2+3+......+n..........so the sum should be: n(n+1)/2............

these proof demonstrates sum of polymise i for i =1 to i=n So wed have 1 +2+3+.....n= n(n+1)/2

Triangular numbers {n(n+1)}/2 are half of oblong numbers {n(n+1)}