n=1时,等式左边=1,等式右边=3 - (2+3)/2=1/2,等式成立
假设当n=k时成立,1/2 + 3/4 +5/8 +...+(2k-1)/2^k = 3 - (2k+3)/2^k
则当n=k+1时,等式左边=1/2 + 3/4 +5/8 +...+(2k-1)/2^k+(2k+1)/2^(k+1)
=3-(2k+3)/2^k+(2k+1)/2^(k+1)
=【-(4k+6)+(2k+1)】/2^(k+1)
=3-(2k+5)/2^(k+1)
=3-【2(k+1)+3】/2^(k+1)
等式成立,得证