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>0,97?	Choose the correct choice from the following answers.
A) 29  B) 30  C) 31  D) 32  E) 33
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 33 is correct answer
<result>E</result>
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>0,97?