求和:1/2*4+1/3*5+1/4*6+,,,+1/(n+1)(n+3)
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1/2*4+1/3*5+1/4*6+,,,+1/(n+1)(n+3)
=1/2*[1/2-1/4+1/3-1/5+1/4-1/6+……+1/(n+1)-1/(n+3)]
=1/2*[1/2+1/3-1/(n+2)-1/(n+3)]
=1/2*[5/6-(2n+5)/(n+2)(n+3)]
=1/2*(5n²+13n)/[6(n+2)(n+3)]
=(5n²+13n)/(12n²+60n+72)
=1/2*[1/2-1/4+1/3-1/5+1/4-1/6+……+1/(n+1)-1/(n+3)]
=1/2*[1/2+1/3-1/(n+2)-1/(n+3)]
=1/2*[5/6-(2n+5)/(n+2)(n+3)]
=1/2*(5n²+13n)/[6(n+2)(n+3)]
=(5n²+13n)/(12n²+60n+72)
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