√(1+1/4²+1/5²)=1+1/(4×5),即1又20分之一.規(guī)律∵1+1/n²+1/(n+1)²=[n²(n+1)²+(n+1)²+n²]/[n²(n+1)²]=[n²(n+1)²+2n(n+1)+1]/[n²(n+1)²]=[n(n+1)+1]²/[n(n+1)]²,∴√[1+1/n²+1/(n+1)²]=[n(n+1)+1]/[n(n+1)]=1+1/[n(n+1)]。故√(1+1/4²+1/5²)=1+1/(4×5)。