Question

Scrieti numarul S=(1x2+2x3+3x4+...+100x101)-5050 ca suma de patrate de numere naturale

Answer 1

Termenii sumei sunt produse de 2 numere consecutive.
Folosesti formula  n*(n+1)= n^2+n


Deci 1*2+2*3+..+100*(100+1) -5050=1^2 + 1+ 2^2 +2 + 3^2 +3 +...+ 100^2 +100 - 5050 =1^2+2^2+3^2+...+100^2 + 1+2+3+...+100 – 5050; (aplicam formula Gauss) =› B=1^2+2^2+3^2+...+100^2 + (100*101)/2- 5050 = 1^2+2^2+3^2+...+100^2 + 5050- 5050 = 1^2+2^2+3^2+...+100^2

Deci e suma de patrate de numere naturale.