碧光环会开花吗:一道高一题

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求和:Sn=(2*2)/(1*3)+(4*4)/(3*5)+…+(2n)*(2n)/(2n-1)*(2n+1)

Sn=(2*2)/(1*3)+(4*4)/(3*5)+…+(2n)*(2n)/(2n-1)*(2n+1)
=1+1/3+1+1/3*5+…+1+1/(2n-1)*(2n+1)
=n+0.5[1-1/3+1/3-1/5+…+1/(2n-1)-1/(2n+1)]
=n+0.5[1-1/(2n+1)]
=n+0.5[2n/(2n+1)]
我想是这样的

Sn=(2*2)/(1*3)+(4*4)/(3*5)+…+(2n)*(2n)/(2n-1)*(2n+1)
=1+1/3+1+1/3*5+…+1+1/(2n-1)*(2n+1)
=n+0.5[1-1/3+1/3-1/5+…+1/(2n-1)-1/(2n+1)]
=n+0.5[1-1/(2n+1)]
=n+0.5[2n/(2n+1)]