Question

Repede, va roog. Dau coroană!​

Answer 1

Explicație pas cu pas:

1/x(x+1) +1/(x+1)(x+2) = (x+2)/x(x+1)(x+2) +x/x(x+1)(x+2)

=(2x+2)/x(x+1)(x+2)= 2(x+1)/x(x+1)(x+2) =2/x(x+2)

2/(x²+4x+4)=2/(x+2)² =>[2/(x²+4x+4)]^(-1)=(x+2)²/2

E(x)= 2/x(x+2) *(x+2)²/2 -1 =>

E(x)=(x+2)/x -1=>E(x)=(x+2-x)/x =>E(x)=2/x

a) 1/a(a+1)= (a+1-a)/a(a+1)= (a+1)/a(a+1)-a/a(a+1)=1/a-1/(a+1) (Adevarat)

c) E(1^-1)+E(2^-1)+E(3^-1)+.....+E(10^-1)=

2/1^(-1) +2/2^(-1)+2/3^(-1)+...+2/10^(-1)=

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

2+2*2+2*3+....+2*10 =

2(1+2+3+...+10)=10*11*2/2=10*11=110