作业帮2^2/(1*3)+4^2/(3*5)+^.+20^2/(19*21)=RT
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2^2/(1*3)+4^2/(3*5)+^.+20^2/(19*21)=RT
2^2/(1*3)+4^2/(3*5)+^.+20^2/(19*21)=
RT
2^2/(1*3)+4^2/(3*5)+^.+20^2/(19*21)=RT
(1+1/3)+(1+1/15)+...+[1+1/(19*21)]=10+1/3+1/15+...+1/(19*21)=10+1/(2^2-1)+1/(4^2-1)+...1/(20^2-1)
如果要具体的答案就麻烦了,大概的步骤是这样的
2^2/1*3
=2^2/(2+1)(2-1)
=2^2/(2^2-1)
=(2^2-1+1)/(2^2-1)
=(2^2-1)/(2^2-1)+1/(2^2-1)
=1-1/(2^2-1)
=1-1/1*3
同理
4^2/(3*5)=1-1/3*5
以此类推
原式=1-1/1*3+1-1/3*5+……+1-1/19*...
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2^2/1*3
=2^2/(2+1)(2-1)
=2^2/(2^2-1)
=(2^2-1+1)/(2^2-1)
=(2^2-1)/(2^2-1)+1/(2^2-1)
=1-1/(2^2-1)
=1-1/1*3
同理
4^2/(3*5)=1-1/3*5
以此类推
原式=1-1/1*3+1-1/3*5+……+1-1/19*21
=10-(1/1*3+1/3*5+……+1/19*21)
=10-[1/2*(1-1/3)+1/2*(1/3-1/5)+……+1/2*(1/19-1/21)]
=10-[1/2*(1-1/3+1/3-1/5+……+1/19-1/21)]
=10-1/2*(1-1/21)
=9又21分之10
收起
10又1/7
算式=2^2/(2^2-1)+4^2/(4^2-1)+^.....+20^2/(20^2-1)
=10+1/(2^2-1)+1/(4^2-1)+^.....+1/(20^2-1)
=10+（1/2）[1/3-1/5]+（1/2）[1/5-1/7]+^.....+（1/2）[1/19-1/21]
=10+(1/2)[1/3+1/21]
=10+1/7
2^2/(1*3)+4^2/(3*5)+^.....+20^2/(19*21)
=1+1/3+1+1/15+1+1/35+……+1+1/399
=10+(1/3+1/15+1/35+……+1/399)
=10+1/2(2/3+2/15+2/35+……+2/399)
=10+1/2(1-1/3+1/3-1/5+1/5-1/7+……+1/19-1/21)
=10+1/2(1-1/21)
=10+1/2*20/21
=10+10/21=220/21