1*2*3/1+2*3*4/1+3*4*5/1+.48*49*50/1简便算法你刚才帮我算了一题帮帮我_数学解答

1*2*3/1+2*3*4/1+3*4*5/1+.48*49*50/1简便算法你刚才帮我算了一题帮帮我

人气：198 ℃　时间：2020-01-09 06:27:49

解答

1/1*2*3+1/2*3*4+.+1/48*49*50
= 1/2 *[(3-1)/(1*2*3)+(4-2)/(2*3*4).+(50-48)/(48*49*50)]
=1/2 * [1/(1*2)-1/(2*3)+1/(2*3)-1/(3*4).+1/(48*49)-1/(49*50)]
=1/2*(1/2-1/2450)
=306/1225