大师作文网求和：Sn=2^/1*3+4^2/3*5+……(2n)^2/(2n-1)(2n+1)
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求和：Sn=2^/1*3+4^2/3*5+……(2n)^2/(2n-1)(2n+1)
Sn=2^/1*3+4^2/3*5+……(2n)^2/(2n-1)(2n+1)
=1+1/1*3+1+1/3*5+...+1+1/(2n-1)(2n+1)
=n+(1/1*3+1/3*5+...+1/(2n-1)(2n+1))
=n+[(1-1/3)/2+(1/3-1/5)/2+...+(1/(2n-1)-1/(2n+1)/2]
=n+(1-1/(2n+1))/2
=n+(2n/(2n+1)/2
=n+n/(2n+1)
=1+1/1*3+1+1/3*5+...+1+1/(2n-1)(2n+1)
=n+(1/1*3+1/3*5+...+1/(2n-1)(2n+1))
=n+[(1-1/3)/2+(1/3-1/5)/2+...+(1/(2n-1)-1/(2n+1)/2]
=n+(1-1/(2n+1))/2
=n+(2n/(2n+1)/2
=n+n/(2n+1)
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