分母有理化
1/(√n+√n-1)
=√n-√(n-1)
1/(2n-1)(2n+1)
=1/2*[(2n+1)-(2n-1)]/(2n-1)(2n+1)
=1/2[(2n+1)/(2n-1)(2n+1)-(2n-1)/(2n-1)(2n+1)]
=1/2[1/(2n-1)-1/(2n+1)]
分母有理化
1/(√n+√n-1)
=√n-√(n-1)
1/(2n-1)(2n+1)
=1/2*[(2n+1)-(2n-1)]/(2n-1)(2n+1)
=1/2[(2n+1)/(2n-1)(2n+1)-(2n-1)/(2n-1)(2n+1)]
=1/2[1/(2n-1)-1/(2n+1)]