Question

1乘3分之1加上3乘上5分之1加上5乘上7分之1。。。。。。。一直加到99乘上101分之1

要过程

Answer 1

1×(1/3)+3×(1/5)+5×(1/7)+...+99×(1/101)
=1/2[(1-1/3)+(1/3-1/5)+(1/5-1/7)+……+(1/99-1/101)]
=1/2(1-1/3+1/3-1/5+1/5-1/7+……+1/99-1/101)
=1/2(1-1/101)
=1/2*(100/101)
=50/101

Answer 2

1/1*3+1/3*5+1/5*7+......+1/99*101
=1/2*(1-1/3)+1/2*(1/3-1/5)+1/2*(1/5-1/7)+......+1/2*(1/99-1/101)
=1/2*(1-1/3+1/3-1/5+1/5-1/7+......+1/99-1/101)
=1/2*(1-1/101)
=1/2*100/101
=50/101

Answer 3

50/101

Answer 4

原式=1/2（1-1/3）+1/2（1/3-1/5）+……+1/2（1/99-1/101）=50/101