Question

Fie functia f:R-R ,f(x) =2x-5. Calculati suma S=f(1)+f(2)+...+f(100)

Answer 1

f(1)=2*1-5=2-5=-3
f(2)=2*2-5=-1
f(3)=2*3-5=1
f(4)=2*4-5=8-5=3
...............
f(100)=100*2-5=200-5=195

f(1)+f(2)+...f(100)=
-3+(-1)+1+3+...+195

Izolam termenii cu minus
1+3+...+195. Gauss pt numere impare, adica 1+3+5+...+2n-1=n*n
2n-1=195
2n=196
n=98
deci suma numerelor pozitive fa fi egala cu 98*98

Faca adunam si numerele negative, vom avea 
-3+(-1)+98*98 = 
-3-1+9604 = 
=9600