Question

a) 1+2-3+4+5-6+7+8-9+...+2008+2009-2010+2011=?

b) 1+2+3-4+5+6+7-9+...+2009+2010+2011-2012​

Answer 1

Răspuns:

Explicație pas cu pas:

a) 1+2-3+4+5-6+7+8-9+...+2008+2009-2010+2011 =

= 0+3+6+9+12+.....+2007 + 2011 =

= 3+6+9+....+2007+2011 = (3+2007)·[(2007-3):3+1]:2 + 2011 =

=(2010:2)·669 + 2011 = 1005·669 + 2011 = 672345+2011 = 674356

b) 1+2+3-4+5+6+7-8+...+2009+2010+2011-2012​ = ?

4+8+12+....+2012 = (4+2012)·[(2012-4):4+1]:2 = 1008·503 = 507024

1+2+3+4+5+6+7+8+.....+2009+2010+2011+2012 =

=(1+2012)·2012:2 = 1006·2013 = 2025078

1+2+3-4+5+6+7-8+...+2009+2010+2011-2012​ =

= 2025078 - 2·507024 = 1011030