这个等式是怎么变过来的？
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原题=左边=
=1/[(3+1)(3-1)]+1/[(5+1)(5-1)]+1/[(7+1)(7-1)]+......+1/[(2n+2)(2n)]
=1/(2×4)+1/(4×6)+1/(6×8)+......+1/[4n(n+1)]
=(1/4)[1/(1×2)+1/(2×3)+1/(3×4)+......+1/n(n+1)]
=(1/4)[1/2+1/2-1/3+1/3-1/4+......+1/n-1/(n+1)]
=(1/4)[1-1/(n+1)]
=n/[4(n+1)]
=右边
=1/[(3+1)(3-1)]+1/[(5+1)(5-1)]+1/[(7+1)(7-1)]+......+1/[(2n+2)(2n)]
=1/(2×4)+1/(4×6)+1/(6×8)+......+1/[4n(n+1)]
=(1/4)[1/(1×2)+1/(2×3)+1/(3×4)+......+1/n(n+1)]
=(1/4)[1/2+1/2-1/3+1/3-1/4+......+1/n-1/(n+1)]
=(1/4)[1-1/(n+1)]
=n/[4(n+1)]
=右边
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