Question

1/(1*3)+1/(2*4)+1/(3*5)+......+1/(48*50)=______

1/(1*3)+1/(2*4)+1/(3*5)+......+1/(48*50)=______

求解答过程。

Answer 1

1/(1×3)=½(1-1/3)，
1/(2×4)=½(1/2-1/4)，
1/(3×5)=½(1/3-1/5)，
……
1/[n×(n+2)]=½[1/n-1/(n+2)]，
……
1/(48×50)=½(1/48-1/50)，
原式=½[1-1/3+1/2-1/4+1/3-1/5+…+1/n-1/(n+2)+…+1/46-1/48+1/47-1/49+1/48-1/50]
=½(1+1/2-1/49-1/50)
=½(1-1/49+1/2-1/50)
=½(48/49+24/50)
=24/49+12/50
=24/49+6/25
=(24×25+6×49)/(49×25)
=894/1225

Answer 2

追答

望采纳，谢谢！

谢谢！

Answer 3

1/(1×3)＝1/2(1－1/3)
1/(2×4)＝1/2(1/2－1/4)
1/(3×5)＝1/2(1/3－1/5)
…
＝1/2(1+1/2－1/49－1/50)
＝1788/2450

Answer 4

几年级题，没超过高二我都能解