找规律计算2/1*3+2/3*5+2/5*7+.+2/97*99+2/99*101
问题描述：
找规律计算2/1*3+2/3*5+2/5*7+.+2/97*99+2/99*101
答
原式=1/1-1/3+1/3-1/5+1/5-1/7…………+1/97-1/99+1/99-1/101
=(1/1-1/3)+(1/3-1/5)+(1/5-1/7)+……+(1/99-1/101)
=1+(1/3-1/3)+(1/5-1/5)+……+(1/99-1/99)-1/101
=1-1/101
=100/101
答
原式=1/1-1/3+1/3-1/5+1/5-1/7…………+1/97-1/99+1/99-1/100=1/1-1/100=99/100
答
=(1/1-1/3)+(1/3-1/5)+(1/5-1/7)+……+(1/99-1/101)
=1+(1/3-1/3)+(1/5-1/5)+……+(1/99-1/99)-1/101
=1-1/101
=100/101