Question

AM Nevoie urgent!!!!!!!
1) Calculați folosind sumele Gauss:
S1= 20+23+26+.......+254+257.

S2=2-4+6-8+10-12+....+98-100.

Answer 1

[tex]\text{E cam greu cu suma lui Guass,dar am sa incerc.}\\ S_1=20+23+26+_{\dots}+254+257\\ S_1=20+(20+3\cdot 1)+(20+3\cdot 2)+_{\dots}+(20+3\cdot 78)+(20+3\cdot 79)\\ S_1=20\cdot 80+3(1+2+3+...+79)\\ S_1=1600+3\cdot \dfrac{79\cdot 80}{2}\\ S_1=1600+3\cdot 79\cdot 40\\ S_1=1600+9480\\ \boxed{S_1=11[tex]S_2=2-4+6-8+10-12+_{\dots}+98-100\\ S_2=2+6+10+_{\dots}+98-4-8-12-_{\dots}-100\\ S_2=2+(4+2)+(4\cdot 2+2)+_{\dots}+(4\cdot 24+2)-4(1+2+3+_{\dots}+25)\\ S_2=2\cdot 25+4(1+2+3+_{\dots}+24)-4\cdot \dfrac{25\cdot 26}{2}\\ S_2=50+4\cdot \dfrac{24\cdot 25}{2}-2\cdot 25\cdot 26\\ S_2=50+1200-1300\\ S_2=50-100\\ S_2=-50[/tex]080}[/tex]