Question

1/1X3+1/3X5+1/5X7+……+1/(2n-1)(2n+1)=?

虽然我知道了答案是n/2n+1，但是我不知道这个过程是怎样的！

Answer 1

很简单1/(2n-1)(2n+1)=[1/(2n-1)-1/(2n+1)]*1/2,然后逐项相加就得到答案了

Answer 2

1/1X3+1/3X5+1/5X7+……+1/(2n-1)(2n+1)

=1/2×[1-1/3+1/3-1/5+1/5-1/7+……+1/(2n-1)-1/(2n+1)]
=1/2×[1-1/(2n+1)]
=1/2×2n/(2n+1)
=n/(2n+1)