What least fraction should be added to
1/(2 × 3) + 1/(3 × 4) + 1/(4 × 5) + ....... + 1/(21 × 22)
so that the result is unity?  Choose the correct choice
A) 5 / 11  B) 6 / 11  C) 4 / 11  D) 7 / 11  E) 8 / 11

Rationale: explanation : given expression = 1 / ( 2 × 3 ) + 1 / ( 3 × 4 ) + 1 / ( 4 × 5 ) + . . . . . . + 1 / ( 21 × 22 ) = ( 1 / 2 - 1 / 3 ) + ( 1 / 3 - 1 / 4 ) + ( 1 / 4 - 1 / 5 ) + . . . . . . . . . . = ( 1 / 21 - 1 / 22 ) = 1 / 2 - 1 / 22 = 10 / 22 = 5 / 11 thus , least fraction to be added = 1 - 5 / 11 = 6 / 11 answer : option b
Answer: B