2005/1*3+2005/3*5+2005/5*7+···2005/99*101=?如题
问题描述：
2005/1*3+2005/3*5+2005/5*7+···2005/99*101=?如题
也就是1乘3分之2005
答
2005/1*3+2005/3*5+2005/5*7+···2005/99*101 = 2005 / [1/(1*3) + 1/(3*5) + 1/(5*7) + .+ 1/(99*101)] = 2005 / [(1- 1/3)/2 + (1/3 - 1/5)/2 + (1/5 - 1/7)/2 + .+ (1/99 - 1/101)/2] = 2005 / { [ (1 - 1/3) + (1/3 - 1/5) + (1/5 - 1/7) + .+ (1/99 - 1/101)] / 2} = 2005 / { [ 1 + (-1/3 + 1/3) + (-1/5 + 1/5) + (-1/7 + .+ 1/99) - 1/101] /2} = 2005 / { [ 1 - 1/101] / 2} = 2005 / { [ 100/101] / 2} = 2005 / { 50 /101} = 2005 * {101/50} = 4050.1