1. Cho (Un) với Un = 1/(1.3) + 1/(3.5) + …+ 1/[(2n-1).(2n+1)]. Tìm lim Un
2. Tìm lim [căn(1+5+…+(4n-3)) / (2n-1)]
1. Cho (Un) với Un = 1/(1.3) + 1/(3.5) + …+ 1/[(2n-1).(2n+1)]. Tìm lim Un
2. Tìm lim [căn(1+5+…+(4n-3)) / (2n-1)]
1.
`lim[ 1/(1.3) + 1/(3.5) + …+ 1/((2n-1).(2n+1))]`
`=lim[1/2(1-1/(2n+1)]`
`=lim(2n)/(2(2n+1))`
`=lim n/(2n+1)`
`=1/2`
2.
`lim sqrt(1+5+…+(4n-3)) / (2n-1)`
`=limsqrt((n(4n-2))/(2))/(2n-1)`
`=lim sqrt(n/(2n-1))`
`=sqrt(1/2)=sqrt2/2`