1/(2*4)+1/(4*6)+1/(6*8)+...6+1/[(2n-4)*(2n-2)]+1/[(2n-2)*2n

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1/(2*4)+1/(4*6)+1/(6*8)+...6+1/[(2n-4)*(2n-2)]+1/[(2n-2)*2n
1/(2*4)+1/(4*6)+1/(6*8)+...6+1/[(2n-4)*(2n-2)]+1/[(2n-2)*2n

1/(2*4)+1/(4*6)+1/(6*8)+...6+1/[(2n-4)*(2n-2)]+1/[(2n-2)*2n
1/(2*4)+1/(4*6)+1/(6*8)+...6+1/[(2n-4)*(2n-2)]+1/[(2n-2)*2n
1/2(1/2-1/4+1/4-1/6+1/6-1/8+...+1/2n-2-1/2n)
=1/2(1/2-1/2n)
=(n-1)/4n