The sequence of numbers a1, a2, a3, ..., an is defined by an = 1/n - 1/(n+2) for each integer n >= 1. What is the sum of the first 30 terms of this sequence?  Choices:
A) 1/30-1/32  B) 1 - (1/30 + 1/30)  C) (1+1/2) – (1/31 +1/ 32)  D) 1 - 1/32  E) 1/32-1/30
The answer would most certainly be[C]. But the question needs a slight modification.n&gt;=1, since the answer does consider a1 under the sum.   The sequence is :   a1 = 1-1/3   a2 = 1/2 - 1/4   a3 = 1/3 - 1/5....   We can observe that the third term in the sequence cancels the negative term in the first. A similar approach can be seen on all the terms and we would be left with 1 + 1/2 from a1 and a2 along with -1/32 and -1/31 from a30 and a29 term which could not be cancelled.   Hence the sum = (1+1/2) – (1/31 +1/ 32)   Answer : (1+1/2) – (1/31 +1/ 32)
<result>C</result>
The sequence of numbers a1, a2, a3, ..., an is defined by an = 1/n - 1/(n+2) for each integer n >= 1. What is the sum of the first 30 terms of this sequence?