Question

(2+4+6+••••+288)-144 plis ca mâine am test si nu înțeleg nimica

Answer 1

Răspuns:

2(1+2+3+...+144)-144=

=2[(144*145)/2] -144=

Suma lui Gaus

=20880-144=20736 =

Answer 2

 

$\displaystyle\bf\\(2+4+6+...+288)-144=?\\\\Calculam~numarul~de~termeni~din~suma.\\\\n=\frac{288-2}{2}+1=\frac{286}{2}+1=143+1=144~de~termeni\\\\Aplicam~formula~lui~Gauss.\\\\S=\frac{n(ultimul~termen + primul~termen))}{2}\\\\S=\frac{144(288+2)}{2}\\\\Rezolvam~exercitiul:\\\\(2+4+6+...+288)-144=\frac{144(288+2)}{2}-144=\\\\=\frac{144\times290}{2}-144=\\\\=144\times145-144=144(145-1)=144\times144=\boxed{\bf144^2}=\boxed{\bf20736}$