初一代数找数的规律求值:S=(1+1/1*2)+(2+1/2*3)+(3+1/3*4)+……+(20+1/20*21)

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初一代数找数的规律求值:S=(1+1/1*2)+(2+1/2*3)+(3+1/3*4)+……+(20+1/20*21)

初一代数找数的规律求值:S=(1+1/1*2)+(2+1/2*3)+(3+1/3*4)+……+(20+1/20*21)
初一代数找数的规律
求值:S=(1+1/1*2)+(2+1/2*3)+(3+1/3*4)+……+(20+1/20*21)

初一代数找数的规律求值:S=(1+1/1*2)+(2+1/2*3)+(3+1/3*4)+……+(20+1/20*21)
S=1+2+3+·····+20+1- 1/2 + 1/2 - 1/3 + 1/3 - 1/4 +1/4 - 1/5·····+ 1/20 -1/21 =1+2+3+······+20+1-1/21=210+20/21

由题得
S=(1+2+3+...+20)+(1/1*2+1/2*3+1/3*4+...+1/20*21)
=(1+20)*20/2+1-1/2+1/2-1/3+1/3-...+1/20-1/21
=210+1-1/21
=211-1/21
=4430/21

s=(1+2+3+4+5+...+20)+(1-1/2+1/2-1/3+1/3-1/4+1/4.....+1/20-1/21)
=(1+20)*20÷2+1-1/21
=210又20/21