Question

S=1+2+3..+60 S=4+8+12+...+100 S=2+4+6...+18

Answer 1

S=1+2+3+...=60=60*61/2=1830

S=4+8+12+...+100=4(25*26/2)=1300

S=2+4+6+...+18=2(9*10/2)=90

Answer 2

$\displaystyle a).1+2+3+...+60= \frac{60(60+1)}{2} = \frac{60 \times 61}{2} = \frac{3660}{2} =1830 \\ \\ b).4+8+12+...+100=4(1+2+3+...+25)=4 \times \frac{25(25+1)}{2} = \\ \\ =4 \times \frac{25 \times 26}{2} =4 \times \frac{650}{2} =4 \times 325=1300 \\ \\ c).2+4+6+...+18=2(1+2+3+...+9)=2 \times \frac{9(9+1)}{2} = \\ \\ =2 \times \frac{9 \times 10}{2}=\not 2 \times \frac{90}{\not 2} =90$