a) 2+3+4+...+50= aplicam suma lui Gauss
[tex] \frac{50(50 + 1)}{2} = \frac{50 \times 51}{2} = 25 \times 51 = 1275[/tex]
1275-1=1274
b) 1+2+3+....+500= aplicam suma lui gauss
[tex] \frac{500(500 + 1)}{2} = \frac{500 \times 501}{2} = 250 \times 501 = 125250[/tex]
c) 1+97+2+999+3+198=
(1+999)+(97+3)+(198+2)=
1000+100+200=1300
d)1+2+3+...+124= aplicam suma lui gauss
[tex] \frac{124(124 +1)}{2} = \frac{124 \times 125}{2} = 62 \times 125 = 7750[/tex]
e) 2+4+6+...+600=
2(1+2+3+....+300) )= aplicam suma lui gauss pentru: 1+2+3+....+300=
[tex] \frac{300(300 + 1)}{2} = \frac{300 \times 301}{2} = 150 \times 301 = 45150[/tex]
2×45150= 90300
f)15+16+17+...+70=
(15+16+17+...+70) - (1+2+3+...+14)
aplicam suma lui gauss
•15+16+17+....+70=
[tex] \frac{70(70 + 1)}{2} = \frac{70 \times 71}{2} = 35 \times 71 = 2485[/tex]
•1+2+3+...+14=
[tex] \frac{14(14 + 1)}{2} = \frac{14 \times 15}{2} = 7 \times 15 = 105[/tex]
2485-105=2380
g)5+6+7+...+81=
(5+6+7+...+81) - (1+2+3+4)
aplicam suma lui gauss
•5+6+7+...+81=
[tex] \frac{81(81 + 2)}{2} = \frac{81 \times 82}{2} = 81 \times 41 = 3321[/tex]
•1+2+3+4=10
3322-10=3312
h)1+2+3+...+512= aplicam suma lui gauss
[tex] \frac{512(512 + 1)}{2} = \frac{512 \times 513}{2} = 256 \times 513 = 131328[/tex]
i)317+318+319+...+400=
(317+318+319+...+400) - (1+2+3+...+316)
aplicam suma lui gauss
[tex] \frac{400(400 + 1)}{2} - \frac{316(316 + 1)}{2} = \frac{400 \times 401}{2} - \frac{316 + 317}{2} \\ = 200 \times 401 - 158 \times 317 = \\ 80200 - 50086 = 30114[/tex]
