已知x0=0,x1=1,xn+1=(xn+xn-1)/2,求n→无穷大时数列xn的极限

问题描述:

已知x0=0,x1=1,xn+1=(xn+xn-1)/2,求n→无穷大时数列xn的极限

x(n+2) = [x(n+1)+x(n)]/2,x(n+2) - x(n+1) = -[x(n+1)-x(n)]/2,{x(n+1)-x(n)}是首项为x(1)-x(0)=1,公比为(-1/2)的等比数列.x(n+1)-x(n) = (-1/2)^n, n=0,1,2,..x(n+2) + x(n+1)/2 = x(n+1) + x(n)/2,{x(n+1) + x(n)...