Question

astept raspuns
calculati S=(1+3+5+...+2013) - (2+4+6+...+2012).

Answer 1

(1+3+5+...+2013) -2(1+2+3+....+1006)

S1 =1 +3 +5+...+2013=

(2013-1):2 +1 =  2012:2 +1= 1006+1=1007 termeni

S1=(1+2013)*1007/2

S1=2014 *1007/2

S1=1007*1007

S1=1007²

S2=2(1+2+3+...+1006)

S2=2(1+1006)*1006/2

S2= 1007*1006

S1-S2=  1007² -1007*1006=  1007(1007-1006)=  1007 *1= 1007