How much is 1 × 3 / 1 plus 3 × 5 / 1 plus 97 × 99 / 1 fast

1/(1×3)+1/(3×5)+…… +1/(97×99)
=1/2×[2/(1×3)+2/(3×5)+…… +2/(97×99)]
=1/2×(1-1/3+1/3-1/5+…… +1/97-1/99)
=1/2×(1-1/99)
=1/2×98/99
=49/99

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