Question

f:R->R; f(x)= -x²+8x
Calculati f(1)+f(2)+...+f(10)

Answer 1

Răspuns:

f(x)= -x²+8x

f(1)=-(1)²+8*1=-1+8

f(2) =-2²+8*2

f(3)= -3²+8*3

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

f(10)= -10²+8*10

f(1)+f(2)+f(3)+...+f(10)=

-1²-2²-3²-...-10²+8(1+2+...+10)=

-(1²+2²+...+10²)+8*10*11/2(suma  gauss)=440

Pt  prima  paranteza  folosesti   formula  sumei  patratelor primelor n  numere  naturale

Sn=n(n+1)(2n+1)/6  unde  n=10

S10=10*11*21/6=770

Inlocuiesti si  obtii

-770+440= -330

Explicație pas cu pas: