第1个回答 2022-10-04
1/1*3+1/2*4+1/3*5...+1/2019*2021
=(1/1*3+1/3*5+…+1/2019*2021)+(1/2*4+1/4*6+…+1/2018*2020)
=(1/2-1/6+1/6-1/10+……+1/4038-1/4042)
+(1/4-1/8+1/8-1/12+……+1/4036-1/4040)
=(1/2-1/4042)+(1/4-1/4040)
=2020/4042+1009/4040
=1010/2021+1009/4040
=(4080400+2039189)/8164840
=6119589/8164840本回答被提问者采纳