Question

解三元一次方程组 X+Y-2Z=-3,2X-3Y+2Z=2，-3X+5Y+2Z=13

Answer 1

X+Y-2Z=-3 (1)
2X-3Y+2Z=2 (2)
-3X+5Y+2Z=13 (3)
(1)+(2)
3X-2Y=-1 (4)
(2)-(3)
5X-8Y=-11 (5)
(4)×4-(5)
12X-5X=-4+11
7X=7
所以
X=1
Y=(5X+11)/8=2
Z=(X+Y+3)/2=3

Answer 2

a1=a
a2=2a/(a+1)
a3=2a2/(a2+1)=4a/(3a+1)
a4=2a3/(a3+1)=8a/(7a+1)

a(n+1)=2an/(an+1)
取倒数
1/a(n+1)=(an+1)/2an=1/(2an)+1/2
1/a(n+1)-1=1/(2an)-1/2=1/2(1/an-1)
所以1/an-1等比，q=1/2
1/an-1=(1/a-1)*(1/2)^(n-1)=(1-a)/[a*2^(n-1)]
an=1/[1+(1-a)/[a*2^(n-1)]]=a*2^(n-1)/[a*2^(n-1)-a+1]