Question

n趋于无穷大,1/(1*3)+1/(3*5)+…+1/[(2n-1)(2n+1)]极限

Answer 1

因为1/[(2n-1)(2n+1)]=(1/2)[1/(2n-1)-1/(2n+1)],

所以,原式=lim(1/2)[1-1/3+1/3-1/5+…+1/(2n-1)-1/(2n+1)] n趋于无穷大

=lim(1/2)[1-1/(2n+1)] n趋于无穷大

=1/2