1/2001+2/2001+3/2001.+4001/2001这道题怎么解

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1/2001+2/2001+3/2001.+4001/2001这道题怎么解

1/2001+2/2001+3/2001.+4001/2001这道题怎么解
1/2001+2/2001+3/2001.+4001/2001这道题怎么解

1/2001+2/2001+3/2001.+4001/2001这道题怎么解
=(1+2+……+4001)/2001
=[(1+4001)+(2+4000)+……+(2000+2002)+2001]/2001
=(4002+4002+……+4002+2001)/2001
=(4002×2000+2001)/2001
=(2001×4000+2001)/2001
=2001×(4000+1)/2001
=4000+1
=4001

1+...+4001=2000对(1+4001)相加,再加2001,就等于4000+1=4001

用等差数理公式,(首项+末项)*项数/2,得(1/2001+4001/2001)*4001/2=2*4001/2=4001