[tex]\displaystyle 1+2+3+4+5+6+...+20= \frac{20(20+1)}{2} = \frac{20 \times 21}{2} = \frac{420}{2} =210 \\ \\ 1+2+3+4+...+49= \frac{49(49+1)}{2} = \frac{49 \times 50}{2} = \frac{2450}{2} =1225 \\ \\ 1+2+3+...+100= \frac{100(100+1)}{2}= \frac{100 \times 101}{2} = \frac{10100}{2} =5050 \\ \\ 1+2+3+4+...+200= \frac{200(200+1)}{2} = \frac{200 \times 201}{2} = \frac{40200}{2} =20100 [/tex]
