Question

Calculati sumele: a)1+3+5+...+2011, b)2005+2+4+6+...+4008, c)1996+2+4+6+...+3990, d)22+24+26+...+498

Answer 1

+=plus
=ori
:=impartit
a)
1+3+5+...........+2011=(2011+1)x(numarul de termeni):2
numarul de termeni=(2011-1):2+1=2010:2+1=1005+1=1006
(2011+1)x1006:2=2012x503=1012036
b)
2005+2+4+6+.....+4008
mai intai vom calcula
2+4+6+.........+4008=(4008+2)x(numarul de termeni):2
numarul de termeni=(4008-2):2+1=4006:2+1=2003+1=2004
(4008+2)x2004:2=4010x1002=4018020
4018020+2005=4020025
c)
1996+2+4+6+.........+3990
mai intai vom calcula
2+4+6+.........+3990=(3990+2)x(numarul de termeni):2
numarul de termeni=(3990-2):2+1=3988:2+1=1994+1=1995
(3990+2)x1995:2=3992x997,5=3982020
3982020+1996=3984016
d)
22+24+26+........+498=2x(11+12+13+......+249)=
11+12+13+......+249=(249+11)x(numarul de termeni):2
numarul de termeni=(249-11):1+1=238:1+1=238+1=239
(249+11)x239:2=260x119,5=31070
2x31070=62140