Question

Va rog ajutati-ma dau Cel mai bun raspuns si Multumesc si e pt. 14 de puncte
1.Calculati !
S= 1+2+3+...+80
S=2+4+6+...+100
S=3+7+11+15...+43
S=4+8+12....+2000
S=5+10+15+...+2000
S=7+14+21...+2002
Va rog ajuatati-ma.
Va Multumesc !!!

Answer 1

S = 1+ 2 + 3 + 4 +..........+80
S = 80 + 79 + 78 +...........+1
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2S = 81·80÷2 = 81 ·40      S = 81·20      S = 1620 
S = 2 (1 + 2 + 3 +................50) = 2·50·51÷2 = 2550   
S = 3 + (3 + 4·1) + (3+4·2) +.......+(3 +4·10) = 3·11 + 4(1+ 2 + 3 +....+10) =
= 3·11 + 4·10·11÷2 = 11(3 + 20) = 11·23 = 253
S = 4(1 + 2 + 3 + .....+500) = 4·500·501÷2 = 501000
S = 5(1 + 2 + 3 +.....+400) = 5·400·401÷2 = 401000
S = 7(1 + 2 + 3 +......+286) = 7·286·287÷2 = 287287