Question

1+3+5+........+2017 ​

Answer 1

1+3+5+........+2017 =

= 1+2+3+4+...+2017 - (2+4+6+8+...+2016) =

= 2017•2018:2 -2(1+2+3+4+...+1008)=

= 2017• 1009 -2•1008•1009:2=

=2017•1009-1008•1009=

=1009(2017-1008)=

=1009•1009=

=1009²=

=1018081

Answer 2

Răspuns:

1009²

Explicație pas cu pas:

S=1+3+5+....+2017.

Numarul de termeni:

n=(2017-1)/2+1=2016/2+1=1008+1=1009

Suma este:

S=n(a1+an)/2=1009×(1+2017)/2

S=1009×2018/2=1009×1009=1009²