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Cum se reszolva aceste 2 exerciții 15 si 16.Va rog

Cum Se Reszolva Aceste 2 Exerciții 15 Si 16Va Rog class=

Răspuns :

Renatemambouko
formula pentru suma lui Gauss
1+2+3+...+n=n(n+1)/2
15a)
1+2+3+...+80=80×81/2=3240
15b)
2+4+6+..+100=2(1+2+...+50)=2×50×51/2=2550
15c)
1+3+5+....99=1+2+3+4+....+99-2-4-...-98)=1+2+3+...+99-2(1+2+3+...+49)=
=99×100/2-2×49×50/2=99×50-49×50=50(99-49)=50×50=2500
15d)
3+7+11+15+....+43=3+(3+4)+(3+8)+(3+12)+....+(3+40)=
nr termeni  (43-3):4+1=11
=3×11+(4+8+12+...40)=33+4(1+2+...+10)=33+4×10×11/2=33+220=253

16a)
3+6+9+12+...+2019=3(1+2+3+4+...+673)=3×673*674/2=680403
16b)
 4+8+12+...+2020=4(1+2+3+....+505)=4×505×506/2=511060
16c)
5+10+15+20+...+2020=5(1+2+3+4+...+404)=5×404×405/2=409050
16d)
7+14+21+...+2023=7(1+2+3+...+289)=7×289×290/2=293335

Alte intrebari