问题
填空题
已知n是正整数,P1(x1,y1),P2(x2,y2),…,Pn(xn,yn),…是反比例函数y=
|
答案
易得x1y1=k,x2y2=k,…xnyn=k,且由x2y2=k得到:y2=
,k x2
∵x1=1,x2=2,则A1=x1y2=a=
=x1k x2
,k 2
∴k=2a.
∵xn+1yn+1=k,xn+1=n+1,
∴yn+1=
,k n+1
又∵x1=1,
∴A1•A2•…•An=x1y2•x2y3…xnyn+1=x1(y2•x2)•(y3•x3)y4•xnyn+1=k•k…k×x1yn+1=k•k…k×
=kn-1•k n+1
=k n+1
=kn n+1
.(2a)n n+1