Question

Rezolvaţi prin suma Gauss.
1.S= 1+2+3 ..... +70
2. S= 5+10+15 ..... +200
3. S= 10 +20 + 30...... 100

Answer 1

$\displaystyle a).1+2+3+...+70= \frac{70(70+1)}{2} = \frac{70 \times 71}{2} = \frac{4970}{2} =2485 \\ \\ b).5+10+15+...+200=5(1+2+3+...+40)=5 \times \frac{40(40+1)}{2} = \\ \\ =5\times \frac{40 \times 41}{2} =5 \times \frac{1640}{2} =5 \times 820=4100 \\ \\ c).10+20+30+...+100=10(1+2+3+...+10)= \\ \\ =10 \times \frac{10(10+1)}{2} =10 \times \frac{10 \times 11}{2} =10 \times \frac{110}{2} =10 \times 55=550$