解数学题1/1*3+1/3*5+1/3*7+...+1/99*101=?

解数学题1/1*3+1/3*5+1/3*7+...+1/99*101=?
解数学题1/1*3+1/3*5+1/3*7+...+1/99*101=?

解数学题1/1*3+1/3*5+1/3*7+...+1/99*101=?
=1/2(2/1*3+2/3*5+2/5*7+……+2/99*101)
=1/2(1-1/3+1/3-1/5+1/5-……-1/99+1/99-1/101)
=1/2(1-1/101)
=50/101

1/3*7这里是不是错了？
1/1*3+1/3*5+1/5*7+...+1/99*101
=1/2X【（1-1/3）+（1/3-1/5）+（1/5-1/7）+...+（1/99-1/101）】
=1/2x(1-1/101)
=1/2x100/101
=50/101