Question

Imi puteti rezolva aceste exercitii cu formula gauss

1.Să se calculeze urmatoarele sume :

D) 5+10+15+........+2015 =

E) 1+3+5+......+2015 =

F) 1+6+11+.........+2011=

G) 1+5+9+..........+2013

H) 100+101+102+.......+2014=

VA ROG REPEDE DAU COROANA CELUI CARE LE FACE PRIMUL

Answer 1

D) 5+10+15+........+2015 =
=5(1+2+3+...403)=5×403×404/2=407030

E) 1+3+5+......+2015 =
=1+2+3+4+5+6+.....+2014+2015-2-4-6-....-2014=
=2015×2016/2-2(1+2+3+....+1007)=
=2015×1008-2×1007×1008/2=
=2015×1008-1007×1008=
=1008×(2015-1007)=
=1008×1008=1008²=1016064

 F) 1+6+11+.........+2011=
nr pas 6-1=5
nr termeni (2011-1):5+1=403
termen de mijloc (1+2011)/2=1006
=1006×403=405418

G) 1+5+9+..........+2013=
nr pas 5-1=4
nr termeni (2013-1):4+1=503+1=504
se grupeaza cate 2  1+2013=2014    5+ 2009=2014  si asa mai departe
=2014×504/2=507528

H) 100+101+102+.......+2014=
nr termeni 2014-100+1=1915
=100+(100+1)+(100+2)+(100+1914)=
=100×1915+(1+2+3+....+1914)=
=191500+1914×1915/2=
=191500+1832655=2024155