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

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

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

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