Question

关于二次根式的求助 如何化简根号下1+n方分之1+(n+1)方分之1?

Answer 1

√(1+1/nn+1/(n+1)^2)
=√(nn(n+1)^2 + nn + (n+1)^2) / n(n+1)
=√((nn+1)(nn+1+2n) + nn) / n(n+1)
=√((nn+1)^2 + 2n(nn+1) + nn) / n(n+1)
=(nn+1+n)/ n(n+1)