Se pot folosi formulele:
1+2+3+...+n = n*(n+1) / 2
1+3+5+7+...+2n-1 = n^2
2+4+6+...+2n = n*(n+1)
----------------------------------------- Obs. n = numarul termenilor !
b) a=1+3+5+...+31= 16^2 = 256 ;
ptr. ca ... 2n-1=31 => 2n=32 deci n=16.
c) a=1+3+5+...+2011=1006^2 = 1 012 036 ;
ptr. ca ... 2n-1=2011 deci n=(2011+1):2=1006
d) a=(2+4+6+...+2012)+1007=
2+4+6+...+2012 =1006*1007 (2n=2012 deci n=1006)
a=1006*1007 + 1007 = 1007(1006+1)=1007^2 = 1 014 049 ;
