1x2+2x3+3x4+4x5······100x101答案是几?_数学解答

1x2+2x3+3x4+4x5······100x101答案是几?

人气：470 ℃　时间：2019-09-26 14:42:19

解答

1*2+2*3+3*4+.+100*101
=1/3*1*2*3+1/3[2*3*4-1*2*3]+1/3[3*4*5-2*3*4]+.+1/3[100*101*102-99*100*101]
=1/3[1*2*3+2*3*4-1*2*3+3*4*5-2*3*4+...+100*101*102-99*100*101]
=1/3*100*101*102
=343400