Question

Fie functia f : R→R , f(x)= 8x-7 .
Calculati suma S=f(1) +f(2) +….f(100)
Cu explicatii
Multumesc!

Answer 1

$S=f(1)+f(2)+f(3)+...+f(100)= \\ \\ =(8 \cdot 1-7)+(8 \cdot 2-7)+(8 \cdot 3-7)+...+(8 \cdot 100-7)= \\ \\ =8 \cdot 1 + 8 \cdot 2 + 8 \cdot 3+...+8 \cdot 100-(7+7+7+...+7)= \\ \\ =8(1+2+3+...+100)-700= \\ \\ =8 \cdot \frac{100 \cdot 101}{2}-700= \\ \\ = 40400-700= \\ \\ =39700.$

Answer 2

Observam ca termenii sumei sunt in progresie aritmetica
[tex]a_1=f(1)=1\\ a_{100}=f(100)=800-7=793\\ S_{100}=\frac{(a_1+a_{100})100}{2}=\frac{(1+793)100}{2}=794\cdot50=39700[/tex]