Question

Tìm a biết  : 

( 1-1/3 ) * ( 1-1/6 )  * ( 1-1/10 ) * ( 1-1/15 ) * ... * ( 1- 1/780 ) *a = 1

Answer 1

(1 - 1/3) × (1 - 1/6) × (1 - 1/10) × (1 - 1/15) × ... × (1/780) × a = 1

2/3 × 5/6 × 9/10 × 14/15 × ... × 779/780 × a = 1

4/6 × 10/12 × 18/20 × 28/30 × ... × 1558/1560 × a = 1

1×4/2×3 × 2×5/3×4 × 3×6/4×5 × 4×7/5×6 × ... × 38×41/39×40 × a = 1

1×2×3×4×...×38/2×3×4×5×...×39 × 4×5×6×7×...×41/3×4×5×6×...×40 × a = 1

1/39 × 41/3 × a = 1

41/297 × a = 1

=> a = 297/41

Answer 2

1 - 1/3) × (1 - 1/6) × (1 - 1/10) × (1 - 1/15) × ... × (1/780) × a = 1

2/3 × 5/6 × 9/10 × 14/15 × ... × 779/780 × a = 1

4/6 × 10/12 × 18/20 × 28/30 × ... × 1558/1560 × a = 1

1×4/2×3 × 2×5/3×4 × 3×6/4×5 × 4×7/5×6 × ... × 38×41/39×40 × a = 1

1×2×3×4×...×38/2×3×4×5×...×39 × 4×5×6×7×...×41/3×4×5×6×...×40 × a = 1

1/39 × 41/3 × a = 1

41/297 × a = 1

=> a = 297/41