The Very Quick Problem

Here we have, $100+1=101$ , $99+2=101$ . . . . . . . . $51+50=101$ , 50 such couples adding up to 101.

Therefore the total is $101×50=\boxed{5050}$

There is a general form for such sequences, i.e, $\displaystyle\frac{n×(n+1)}{2}$

Where n is the ending number, therefore the answer is $\displaystyle\frac{100×101}{2}=\boxed{5050}$

That's Gauss' s formula.

$1+2+3+4+...+100=\frac{100 \times 101}{2}=5050$

An easy process...
Let, A=1+2+.....100---(1) A=100+....+2+1---(2)
Now (1)+(2)=> 2A=101+........+101+101 or, A=(101*50)/2 or, A=5050

n(n+1)divided by 2 Where n is no of terms. 100(100+1)÷2

n(n+1)/2

=100*(100+1)/2

=5050.