Question

3+6+9+.........+30

2+4+6+8+......+1998+2000
1+2+3+...........+9
0+1+2+3+4.......+1989

Answer 1

Aici este Suma Gaus
Ea se face in felul urmator
1)3*(1+2+3+4+...+10)=3*10*11/2=165
2)9*10/2=45
3)1989*1990/2=1979055

Answer 2

3+6+9+....+30
S= 3+6+9+...+24+27+30
S=30+27+24+...+9+6+3
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2S=33+33+33+...+33+33+33
... (puncte puncte ) se repeta de 30 ori
S=suma
30*33=990 ( 2 S de acelasi fel )
990:2=435(S)
LA celelalte faci LA fel .
... se repeta de atatea ori cat si nr de LA sfarsitul sirului
Ex. pe care il ai 2+4+...... :
2+4+6+8+...+1998+2000
S=2+4+6+8+...+1994+1996+1998+2000
S=2000+1998+1996+1994+...+8+6+4+2
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2S= 2002+2002+2002+2002+...+2002+2002+2002+2002
....de 2000 ori
2000*2000=4.000.000(2S)
4.000.000:2=2.000.000(Suma)

1+2+3+...+9
S=1+2+3...+7+8+9
S=9+8+7+...+3+2+1
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2S=10+10+10+...+10+10+10
... se repeta de 9 ori
10*9=90(2S)
90:2=45(Suma)

0+1+2+3+4+...+1989
S=0+1+2+3+4+...+1985+1986+1987+1988+
1989
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2S=1.989+1989+1989+1989+1989+..+1989
... se repeta de 1.989 ori
1989*1989=12.444.888(2S)
12.444.888:2=6.222.444(Suma)