Question

Simplify 1-1/3×1-1/4×1-1/5×...................1-1/n

Answer 1

1-1/3 × 1-1/4 × 1-1/5 ×..... × 1-1/n
=> (3-1)/3 × (4-1)/4 × (5-1)/5 ×... × (n-1)/n
=> 2/3×3/4×4/5 ×...× (n-2)/(n-1) × (n-1)/n
=> 2/n
Because, all numbers between 2 and n will be cancel out.
Final solution will be 2/n