calculati sumele:
a)1+3+5+....+2011
b)2005+2+4+6+4008
c)1996+2+4+6+....+3990
d)22+24+26+...+498
Răspunsuri la întrebare
a ) 1 + 3 + 5 + ........ + 2011 =
→ aflam cati termeni are suma:
( 2011 - 1 ) : 2 ( ratia) + 1 = 2010 : 2 + 1 = 1005 + 1 = 1 006 termeni are suma
= 1 006 × ( 1 + 2 011 ) / 2 =
= 1 006 × 2012 / 2 =
= 1 006 × 1006 =
= 1 012 036
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b)
2005 + 2 + 4 + 6 + 4008 = 6 025
= 2005 + ( 4 + 6 ) + ( 2 + 4008 ) = → folosesc asociativitatea adunarii
= 2005 + 10 + 4 010 =
= 6025
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c)
1 996 + 2 + 4 + 6 + ......+ 3 990 =
= 1 996 + 2 × ( 1 + 2 + 3 + .........+ 1 995 ) =
= 1 996 + 2 × 1 995 × 1996 / 2 =
= 1 996 + 1 995 × 1 996 =
= 1 996 ( 1 + 1 995 ) =
= 1 996 × 1 996 =
= 3 984 016
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d)
22 + 24 + 26 + ......... + 498 =
= 2 × ( 11 + 12 + 13 + ...... + 249 ) =
→ aflam cati termeni are suma :
249 - 11 + 1= 238 + 1 = 239 de termeni are suma
= 2 × 239 × ( 11 + 249 ) / 2 =
= 239 × 260 =
= 62 140