`a)`
`A=3/4 ×8/9×15/16× ... ×9999/10000`
`A=(1×3)/(2×2) × (2×4)/(3×3) × (3×5)/(4×4)× ... ×(99×101)/(100×100)`
`A=((1×2×3×...×99) × (3×4×5×...×101))/((2×3×4×...×100) × (2×3×4×...×100))`
`A=101/(100×3)`
`A=101/300`
`b)`
`B=8/9 × 15/16 × 24/25×...×3599/3600`
`B=(2×4)/(3×3) × (3×5)/(4×4) × (4×6)/(5×5)× ... ×(59×61)/(60×60)`
`B=((2×3×4×...×59) × (4×5×6×...×61))/((3×4×5×...×60) × (3×4×5×...×60))`
`B=(2×61)/(60×3)`
`B=61/90`
