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原式=1/(1×3) +1/(3×5) +1/(5×7) +……+1/(49×51)
=1/2×[ 2/(1×3) +2/(3×5) +2/(5×7)+……+2/(49×51) ]
=1/2×[ (1-1/3) +(1/3-1/5) +(1/5-1/7)+……+(1/49-1/51) ]
=1/2×( 1-1/3 +1/3-1/5 +1/5-1/7 +……+1/49-1/51 )
=1/2×( 1 -1/51 )
=1/2×50/51
=25/51
=1/2×[ 2/(1×3) +2/(3×5) +2/(5×7)+……+2/(49×51) ]
=1/2×[ (1-1/3) +(1/3-1/5) +(1/5-1/7)+……+(1/49-1/51) ]
=1/2×( 1-1/3 +1/3-1/5 +1/5-1/7 +……+1/49-1/51 )
=1/2×( 1 -1/51 )
=1/2×50/51
=25/51
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