如题所述
第1个回答 2013-10-19
=(1/2)[2/1*3+2/3*5+2/5*7+2/7*9+……+2/97*99+2/99*101]
=(1/2)[(3-1)/1*3+(5-3)/3*5+(7-5)/5*7+……+(99-97)/97*99+(101-99)/99*101]
=(1/2)[1-1/3+1/3-1/5+1/5-1/7+……-1/97+1/97-1/99+1/99-1/101]
=(1/2)[1-1/101]
=50/101.
=(1/2)[(3-1)/1*3+(5-3)/3*5+(7-5)/5*7+……+(99-97)/97*99+(101-99)/99*101]
=(1/2)[1-1/3+1/3-1/5+1/5-1/7+……-1/97+1/97-1/99+1/99-1/101]
=(1/2)[1-1/101]
=50/101.
第2个回答 2013-10-19
(1/1x1/3)+(1/3x1/5)+(1/5x1/7)……+(1/99x1/101)=1/2(1/1-1/3)+1/2(1/3-1/5)+1/2(1/5-1/7)……+1/2(1/99-1/101)=1/2(1/1-1/3+1/3-1/5+1/5-1/7+……+1/99-1/101)=1/2(1/1-1/101)=50/101
第3个回答 2013-10-19
等于1