数学问题解答1/1*3+1/3*5+1/5*7+1/7*9+1/9*11+1/11*13+1/13*15+1/15*17+1/17*19+1/19*21
问题描述：
数学问题解答1/1*3+1/3*5+1/5*7+1/7*9+1/9*11+1/11*13+1/13*15+1/15*17+1/17*19+1/19*21
答
=1/2(1-1/3+1/3-1/5＋……＋1／19－1／21)
=(1/2)(1-1/21)=5/211/1*3+1/3*5+1/5*7+1/7*9+1/9*11+1/11*13+1/13*15+1/15*17+1/17*19+1/19*21如何简便过程(1/2)(3-1)/1*3=(1/2)(3/1*3-1/1*3)=(1/2)(1-1/3),(1/2)(5-3)/3*5=(1/2)(5/3*5-3/3*5)=(1/2)(1/3-1/5),其余的同样去化