Question

g) 1 + 3 + 5 + ... + 99 =

Answer 1

Salut!

Răspuns:2500

$\bf 1 +3 +5+...+99 =\\\bf{1+2+3+4+5+6+...+98+99} - \bf{(2 +4+6+...+98)}=\\\bf 1+2+3+4+5+6+...+98+99 - 2(1+2+3+...+49)=\\\bf\frac{99\times(99+1)}{2}-\not2\times\frac{49\times(49+1)}{\not2} =\\\bf\frac{99\times1\not00}{\not2}-49\times50 =\\\bf 99\times50 - 49\times50=\\50\times(99-49)=\\\bf 50\times 50=\\\bf \boxed{\bf2500 }$