if t = 1 / ( 1 * 2 ) + 1 / ( 2 * 3 ) + 1 / ( 3 * 4 ) + 1 / ( 4 * 5 ) + . . . . . . . . . 1 / [ n ( n + 1 ) ] , for some positive integer n , what is the smallest value of n such that t > 097 ? Options:
A) 29  B) 30  C) 31  D) 32  E) 33

Rationale: we can break the t as : ( n + 1 - n ) / n ( n + 1 ) - - - - for n = 1 to n 1 / n - 1 / n + 1 plug value , 1,2 . . n we will get a pattern 1 - 1 / 2 - - - for 1 1 / 2 - 1 / 3 - - for 2 1 / 3 - 1 / 4 - - for 4 now work with options . . for 31 , t = 1 - 1 / 32 = 30 / 31 = 0.968 for 32 , t = 1 - 1 / 33 = 0,9696 for 33 , t = 1 - 1 / 34 = 33 / 34 - 0.97 so e is correct answer
Answer: E