Question

Sa se arate ca numarul P=1+3+5+...+1997=?

Answer 1

(1+1)+(3+1)+(5+1)+...+(1+1997)-999=
2+4+6+...+1998-999=
2(1+2+3+...+999)-999=
2(999x1000:2)-999
2(999x500)-999
2x499500-999=999000-999=998001

Answer 2

S=1+3+5+...............1993+1995+1997
S=1997+1995+1993+...........+5+3+1
__________________________________
2S = 1998+1998+1998+..................1998+1998+1998

aflam cate numere se afla in primul sir
1, 1+2*1,1+2*2,...........1+2*998
observam ca sunt  999  numere

2S = 999*1998
2S = 1996002
S = 1996002/2
S  =  998001