wxf2006
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共回答了4434个问题 举报
Cn=1/[(4n-3)(4n+1)]
=1/4*[1/(4n-3)-1/(4n+1)]
Tn=C1+C2+C3+...+Cn
=1/1*5+1/5*9+1/9*13+.....+1/[(4n-3)(4n+1)]
=1/4*[1-1/5]+1/4*[1/5-1/9]+1/4*[1/9-1/13]+.....+1/4*[1/(4n-3)-1/(4n+1)]
=1/4*[1-1/5+1/5-1/9+1/9-1/13+....+1/(4n-3)-1/(4n+1)]
=1/4*[1-1/(4n+1)]
=1/4*4n/(4n+1)
=n/(4n+1)
1年前
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