1/[(2n+1)√(2n-1)+(2n-1)√(2n+1)]
=1/{[√(2n+1)(2n-1)][√(2n+1)+√(2n-1)]}
=(1/2)[√(2n+1)-√(2n-1)]/[√(2n+1)(2n-1)]
=(1/2)[1/√(2n-1)-1/√(2n+1)]
1/(3+√3)+1/(5√3+3√5)+1/(7√5+5√7)
=(1/2)[1/1-1/√3+1/√3-1/√5+1/√5-1/√7)
=(1/2)(1-1/√7)
=(7-√7)/14