Sn=(2/1-2/2/)+(2/2-2/3)+..+(2/n-2/(n+1)) 然后要怎么化简出来?

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Sn=(2/1-2/2/)+(2/2-2/3)+..+(2/n-2/(n+1)) 然后要怎么化简出来?
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Sn=(2/1-2/2/)+(2/2-2/3)+..+(2/n-2/(n+1)) 然后要怎么化简出来?
Sn=(2/1-2/2/)+(2/2-2/3)+..+(2/n-2/(n+1)) 然后要怎么化简出来?

Sn=(2/1-2/2/)+(2/2-2/3)+..+(2/n-2/(n+1)) 然后要怎么化简出来?
直接打开所有括号,重新组合即可.
Sn=(2/1-2/2)+(2/2-2/3)+..+(2/n-2/(n+1))
=2/1-2/2+2/2-2/3+..+2/n-2/(n+1)
=2/1+(-2/2+2/2)+(-2/3+2/3)..+(-2/n+2/n)-2/(n+1)
=2/1-2/(n+1)
=(2n)/(n+1)

Sn=2/1-2/2+2/2-2/3+2/3-2/4+……+2/n-2/(n+1)
中间抵消
=2/1-2/(n+1)
=2n/(n+1)

Sn = 2*(1/1 -1/2) +2*(1/2 -1/3) +2*(1/3 -1/4) +...+2*[1/n -1/(n+1)]
Sn = 2*[1/1 -1/2 +1/2 -1/3 +1/3 -1/4 +...+1/n -1/(n+1)]
Sn = 2*[1 -1/(n+1)]
Sn = 2n/(n+1)