Question

S=3+7+11+...+103
S=4+11+18+...+214

formula lui gauss cu explicatie

Answer 1

$\it \\ \\ 3=3+4\cdot0\\ \\ 7=3+4\cdot1\\ \\ 11=3+4\cdot2\\ \\ \vdots\\ \\ 103=3+4\cdot25$

Suma are 26 de termeni.

Folosind descompunerile de mai sus, se poate scrie:

$\it S=3\cdot26+4(0+1+2+...+25) =3\cdot26+4\cdot\dfrac{25\cdot26}{2}=3\cdot26+2\cdot25\cdot26=\\ \\ = 26\cdot(3+50)=26\cdot53=$