1st term = 1/1 - 1/(1 + 1) = 1/1 - 1/2guerrero wrote:The sequence x1, x2, x3,..., is such that Xn = 1/n - (1/(n+1)). What is the sum of the first 100 terms of the sequence?
2nd term = 1/2 - 1/(2 + 1) = 1/2 - 1/3
3rd term = 1/3 - 1/(3 + 1) = 1/3 - 1/4
4th term = 1/4 - 1/(4 + 1) = 1/4 - 1/5
...
we can see that if we keep adding each term, second part of each term will be cancelled by the first part of the next term. Eventually the sum will be equal to (first part of 1st term - second part of last term).
Hence, sum of first 100 terms = 1/1 - 1/(100 + 1) = 1 - 1/101 = 100/101
The correct answer is C.
