因为1+1/n²+1/(n+1)²=[n²(n+1)²+(n+1)²+n²]/[n²(n+1)²]=[n(n+1)+1]²/[n(n+1)]²,
所以√[1+1/n²+1/(n+1)²]=[n(n+1)+1]/[n(n+1)],
因此√[1+1/4²+1/5²]=(4*5+1)/(4*5)=21/20.