Question

2. Se consideră expresia E(x) = (2x-3)²-3(x-1)(x+1)-5(2-3x), unde x este nr real
b) Demonstreaza ca suma ......
$\frac{1}{ e(0)} + \frac{1}{e(1)} + ... + \frac{1}{e(8)} + 0.1$
este nr natural

$e(x) = {x}^{2} + 3 x + 2$
Vă rog ajuați mă ​

Answer 1

a)E(x)=4x²-12x+9-3(x²-1²)-10+15x=4x²+3x-1-3x²+3=x²+3x+2.

b)E(0)=0+0+2=2.

E(1)=1+3+2=6.

E(2)=4+6+2=12.

E(3)=9+9+2=20.

E(4)=16+12+2=30.

E(5)=25+15+2=42.

E(6)=36+18+2=56..

E(7)=49+21+2=72.

E(8)=64+24+2=90.

S=(1/2+1/6+1/12+1/20+1/30)+(1/42+1/56)+(1/72+1/90)+0,1=

30+10+5+3+2/60 + 4+3/168 + 5+4/360+0,1=

5/6 + 1/24 + 1/40+0,1=

20+1/24 + 1/40+0,1=

7/8 + 1/40 +0,1=

35+1/40 +0,1=

36/40 +0,1=

9/10+0,1=0,9+0,1=1 este nr nat