数列求和如果an>0,a1=1,an^2-(an-1)^2=(an-1)*an,如果an>0,a1=1,an^2-(an-1)^_数学解答

数列求和如果an>0,a1=1,an^2-(an-1)^2=(an-1)*an,
如果an>0,a1=1,an^2-(an-1)^2=(an-1)*an,那么1/(a1+a2) +1/(a2+a3) +……+1/(an-1+an) =

人气：206 ℃　时间：2020-06-25 17:25:16

解答

n≥2时,an²-a(n-1)²=a(n-1)anan²-ana(n-1)=a(n-1)²等式两边同除以a(n-1)²[an/a(n-1)]²-[an/a(n-1)]=1[an/a(n-1) -1/2]²=5/4an/a(n-1) -1/2=√5/2或an/a(n-1) -1/2=-√5/2(舍去)a...