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(1+1/1×3)×(1+1/2×4)×(1+1/3×5)×(1+1/4×6)×……×(1+1/97×99)×(1+1/98×100)
=(1×1+1×1/3)×(2×1/2+1/2×1/4)×(3×1/3+1/3×1/5)×(4×1/4+1/4×1/6)×……×(97×1/97+1/97×1/99)×(98×1/98+1/98×1/100)
=[1×(1+1/3)]×[1/2×(2+1/4)]×[1/3×(3+1/5)]×[1/4×(4+1/6)]×……×[1/97×(97+1/99)]×[1/98×(98+1/100)]
=(2²/3×3²/4×4²/5×5²/6×……×98²/99×99²/100)/(1×2×3×4×……×97×98)
=(2²×3²×4²×5²×……×98²×99²)/(1×2×3²×4²×……×97²×98²×99×100)
=(2×99)/(1×100)
=198/100
=(1×1+1×1/3)×(2×1/2+1/2×1/4)×(3×1/3+1/3×1/5)×(4×1/4+1/4×1/6)×……×(97×1/97+1/97×1/99)×(98×1/98+1/98×1/100)
=[1×(1+1/3)]×[1/2×(2+1/4)]×[1/3×(3+1/5)]×[1/4×(4+1/6)]×……×[1/97×(97+1/99)]×[1/98×(98+1/100)]
=(2²/3×3²/4×4²/5×5²/6×……×98²/99×99²/100)/(1×2×3×4×……×97×98)
=(2²×3²×4²×5²×……×98²×99²)/(1×2×3²×4²×……×97²×98²×99×100)
=(2×99)/(1×100)
=198/100
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