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Fie functia f:R-R, f(x)=3x. Sa se calculeze suma f(1)+f(2)+f(3)+...+f(20).

Răspuns :

CosmyCrina

f(x)=3x

f(1)=3*1

f(2)=3*2

f(3)=3*3

...............

f(20)=3*20

...................+

S=3*1+3*2+3*3+...+3*20

S=3(1+2+3+...+20)

S=3*[tex](\frac{20(20+1)}{2} )[/tex]

S=[tex]3*(\frac{20*21}{2} )[/tex]    (simplificam 20 cu 2)

S=3*(10*21)

S=3*210

S=630

f(1)+f(2)+f(3)+...+f(20)=

=3×1+3×2+3×3+....+3×20=

=3×(1+2+3+...+20)=

=3×(20×21)/2=

=3×10×21=

=30×21=630