Question

1.Afla numarul n∈N* astfel incat $\frac{1}{1 ori 2} + \frac{1}{2 ori 3} +.....+ \frac{1}{n(n+1)} = \frac{100}{101}$ Rasppuns corect 100 vreau rezolvarea.
2.Calculeaza n=$( \frac{ 5\sqrt{3} }{ \sqrt{8} } + \frac{3 \sqrt{3} }{ 5\sqrt{2} } - \frac{7 \sqrt{3} }{ \sqrt{2} } ): \sqrt{3}$ si apoi determina partea intreaga a numarului n√2.
Raspuns corect -4+rezolvarea
3.Daca x-$\frac{1}{x}$=3 ,x≠0,afla cat reprezinta x²+$\frac{1}{x^{2} }$ din 300
Raspuns corect 3,(6)

Answer 1

ai rezolvarile atasate
 ex 1 s-a mai facut aicide f.multe ori daca e neclar il mai gasesti..
2, cam uaratel am ales si eucea mai scurta cale
3. e o aplicatie clasica la binomul la patrat

Answer 2

1/1·2=1/1-1/2
1/2·3=1/2=1/3
......................
1/n·(n+1)=1/n-1/(n+1)

1/1-1/2+1/2-1/3+....1/n-1/(n+1)=100/101
1/1-1/(n+1)=100/101
(n+1-1)/(n+1)=100/101
n/(n+1)=100/101
n=100

2
n=(5√3/√8+3√3/5√2-7√3/√2):√3 =
=5/2√2+3/5√2-7/√2 =
=1/√2( 5/2+3/5-7) =
=1/√2( 25+6-70)/10 =
=1/√2( -39/10 )=
=√2/2( -39/10 )=
=-39√2/20
n√2=-39√2/20 ×√2=-39/10=-3,9
[-3,9]=-4

3.
x-1/x=3    
(x-1/x)²=9
 x²-2×x×1/x+1/x²=9
 x²-2+1/x²=9
 x²+1/x²=11 
11:300=0,03(6) = 3,(6)%